On Actuality Entailments, Causation, and Telicity in Balkar

Abstract

This paper presents a study of actuality entailments in Balkar (a dialect of Karachay-Balkar, Turkic). The study focuses on the deontic and causal meanings of four morphemes: two suffixes (the causative suffix and the suffix -al (‘can/may’)) and two verbs (bujur (‘order’) and qoj (‘allow’)). In the first half of the paper, I provide empirical support for three generalizations: (a) only causal modals can have actuality entailments (all universal and some existential causal modals); (b) actuality entailments arise whenever a causal modal has a telic interpretation, more precisely, when it is not embedded under an imperfective or a delimitative operator (c) existential but not universal causal modals trigger an anti-actuality entailment under negation. In the second half of the paper, I propose a theory of root modality within the framework of situation semantics. In this framework, root modals describe a situation (the anchor situation) and quantify over situations that stand in a particular semantic relation to it. The proposed Causal Modality Theory (CMT) consists of two assumptions: (a) Causal modals quantify over causal chains initiated by the counterparts of the anchor situation. (b) Some existential causal modals have a conditional presupposition: if any counterpart of the anchor situation caused another situation, then the anchor situation itself caused the same situation. The first assumption explains why all universal causal modals have actuality entailments and why existential causal modals trigger an anti-actuality entailment under negation. The second assumption predicts that some existential causal modals (the ones with the conditional presupposition) also trigger an actuality entailment. CMT treats causal modals as bi-eventive predicates, like (non-culminating) accomplishments. They describe two situations: the anchor situation and a situation caused by it. As a result, causal modals are predicted to behave like (non-culminating) accomplishments, namely, they are predicted to trigger actuality entailments if and only if they are not embedded under an imperfective or a delimitative operator.

1. Introduction

1.1. Three Contrasts

In this paper, I present a study of actuality entailments in Balkar (a dialect of Karachay-Balkar, spoken in the Republic of Kabardino-Balkaria, Russia).1 The paper focuses on two verbs and two suffixes with root modal meanings (deontic and causal): the causative suffix and the suffix -al (‘can/may’), glossed as ‘poss’, and two verbs, bujur (‘order’) and qoj (‘allow’).

The phenomenon of actuality entailments was first discussed by Thalberg (1969) and can be illustrated with three contrasts. First, consider (1).

(1)	a.	According to the rules established at the beginning of the meeting, we had to go outside three times while it lasted (but we did not).
	b.	Because the air in the room was stuffy during the meeting, we had to go outside three times while it lasted (#but we did not).

The sentence in (1a) contains a universal modal operator, have to, in an episodic aspectual context with a deontic root interpretation (which is made salient by the adverbial according to the rules). This sentence has no actuality entailment: it does not entail that the prejacent of the modal (‘we go outside three times while it lasted’) is true in the actual world and can be felicitously continued by but we did not. The sentence in (1b) contains the same universal modal operator, have to, in the same aspectual context but with a causal root interpretation (which is made salient by the because clause). This sentence does trigger an actuality entailment: it entails that the prejacent of the modal is true in the actual world and cannot be felicitously continued by but we did not. Thus, some modal flavors give rise to actuality entailments, while others do not (see Bhatt 1999; Hacquard 2006; Mari 2016, among others).

Second, consider the contrast in (2).

(2)	a.	Because of her training, Rosa was able to hit the target (but yesterday, during the competition, she did not).
	b.	Yesterday, during the competition, because of her training, Rosa was able to hit the target (#but she did not).

In (2a), an existential modal operator, be able to, with a causal interpretation (made salient by the because clause) is put in a generic aspectual context, and the sentence has no actuality entailment, that is, it can be continued by but she did not without contradiction. In (2b), the same existential modal operator, be able to, with a causal interpretation is put in an episodic aspectual context, and the sentence has an actuality entailment, that is, it cannot be continued by but she did not without contradiction. Thus, some aspectual contexts (in particular, the episodic perfective) trigger actuality entailments, while others do not (see Bhatt 1999; Hacquard 2006; Homer 2010, and others).

Third, consider the contrast in (3).

(3)	a.	Yesterday, at the competition, because she had not slept the night before, she was not able to hit the target (#but she did).
	b.	Because the air in the room was fine during the meeting yesterday, I did not have to go outside (but I did).

In (3a), an existential modal, be able to, with a causal interpretation is negated, and the sentence gives rise to an anti-actuality entailment: it entails that the prejacent of the modal (‘she hit the target’) is false in the actual world and cannot be felicitously continued by but she did. In (3b), a universal modal, have to, with a causal interpretation is negated, and the sentence has no anti-actuality entailment: it does not entail that the prejacent is false and can be felicitously continued by but I did. Thus, some causal modals trigger an anti-actuality entailment under negation, while others do not.

1.2. Descriptive Definitions

Before elaborating on the three contrasts above, I will establish some basic definitions and assumptions concerning modal operators that I use throughout the paper.

First, a modal operator or a modal, like could or have to in (4), takes the speaker from the actual world to a set of possible ones (see Heim and von Fintel 2010, pp. 29–47). In what follows, I assume that modals are quantifiers over possible situations with variable domain of quantification specified by the context (see Kratzer 1977, 1981, 2006, and subsequent work). The prejacent of a modal operator is its syntactic complement. For instance, in (4), it is the verb phrase process tourist visas in 30 days.

(4)

For three years, Canada could/had to process a tourist visa in 30 days.

Second, I assume that modals are ’anchored to situations’, that is, they introduce and describe a situation, and after they take their prejacent as a complement, they return a predicate of situations, not a proposition (see Kratzer 2006, 2007; Moulton 2015, and others). In what follows, I call anchor situation the situation introduced by a modal operator. For example, in (4), the anchor situation is a particular state of the Canadian immigration system that lasted three years. Root modals like could and have to introduce their own situation (or event) variable distinct from their prejacent, which is evident from the fact that they can be modified by temporal adverbials, as in (4).2

Third, an accessibility relation or modal flavor is understood as the semantic relation between the anchor situation and the situation described by the prejacent of the modal. In (4), for example, it is the relation between the state of the Canadian immigration system that lasted three years and a possible situation of Canada processing a tourist visa that lasts 30 days. More precisely, an accessibility relation is the semantic relation between the anchor situation and the set of situations that the modal quantifies over. In other words, an accessibility relation determines the domain of quantification for a modal operator. The domain of quantification or the set of situations that a modal quantifies over is called modal base. Following Kratzer (1977, 1981), I assume that the accessibility relation and, consequently, the modal base are determined by the context and can be made salient by various adverbials (e.g., because clauses). Modal force is the force of a modal quantifier, typically either existential (e.g., could) or universal (e.g., have to). The two basic types of modal flavors are epistemic (the anchor situation describes the state of someone’s knowledge/picture of the world) and root (all the other flavors). In this paper, I focus on root modals.

Fourth, throughout the paper, I treat causal meanings like make or let as modal operators with universal force and existential force, respectively, and a causal accessibility relation. Let us take, for example, the two English sentences in (5).

(5)	a.	Rosa made Karl enter the building (#but she did not let him do it).
	b.	Rosa let Karl enter the building (but she did not make him do it).

In both (5a) and (5b), the anchor situation is a situation where Rosa does or does not do something (‘causation by action’ vs. ‘causation by omission’; see Raffy 2021, pp. 14–18 for discussion). The prejacent is the verb phrase Karl enter the building. The relation between the anchor situation and the situation specified by the prejacent is causal. Both (5a) and (5b) allow for a counterfactual inference (see Dowty 1979; Lewis 1973, and others): if Rosa had not done whatever she did, Karl would not have entered the building.3

Apart from notions related to modality, I also rely on several notions related to aspect and Aktionsart.

First, accomplishments, like the verb phrase open the door in (6), are here analyzed as predicates that describe a complex situation consisting of two sub-situations related by a causation relation4 (see Dowty 1979; Kratzer 2005; Levin and Rappaport-Hovav 1995; Maslov 1948; Vendler 1957; Paducheva 2004, 2009; Ramchand 2008; Tatevosov 2015, and others).5 In (6a), there are a situation where Rosa does something and a situation of the door being opened.

(6)	a.	Rosa opened the door (#but the door did not open).
	b.	Rosa was opening the door (but the door did not open).

Second, one of the key properties of accomplishments is that they give rise to a culmination entailment whenever they have a telic interpretation, which is an entailment that the caused situation took place in the actual world. This entailment is present in some aspectual contexts but not in others (see Bach 1986; Bennett and Partee 1972; Dowty 1979; Klein 1994; Landman 1992; Parsons 1990, among many others). In particular, accomplishments trigger an obligatory culmination entailment under the perfective aspect, as in (6a), which entails that the door was open, but not under the progressive aspect, as in (6b), which does not entail that the door was open.

Third, non-culminating accomplishments (for the term, see Bar-el et al. 2005; Copley and Wolff 2014; Tatevosov 2008, and others), like the verb phrase read the letter in (7), have both a telic interpretation and an atelic interpretation under the perfective aspect. Whenever they have a telic interpretation, they also give rise to a culmination entailment (the sentence in (7a) entails that the letter was read until the end). The caused situation here (‘the letter was read until the end’) can be identified as the resultant state in the terms of Kratzer (2000).

(7)	a.	Rosa read the letter in five minutes (#but she did not finish it).
	b.	Rosa read the letter for five minutes (but she did not finish it).
	c.	Rosa was reading the letter (but she did not finish it).

Various approaches to the culmination entailment of accomplishment predicates can be grouped into two large categories. According to the first type of theories (e.g., Bar-el et al. 2005; Dowty 1979; Landman 1992; Parsons 1990; Tatevosov 2008; Tatevosov and Ivanov 2009), the culmination entailment is present in the base meaning of both accomplishments, like the verb phrase open the door, and non-culminating accomplishments, like the verb phrase read the letter, and can be canceled by some aspectual operators, including the episodic imperfective, like in (6b) and (7c), and a silent delimitative operator, presumably used in (7b). The delimitative operator is silent in English but can be overt in other languages (cf. the delimitative prefix po- in Russian).

According to the second type of theories (e.g., Copley and Harley 2015; Copley and Wolff 2014; Levin and Rappaport-Hovav 2001), the culmination entailment is not present in the base meaning of accomplishments but rather arises from the combination of an accomplishment predicate and some aspectual operators, like the perfective.

In what follows, I take the former view and assume that the culmination entailment is present in the base meaning of all accomplishments (including both open the door and read the letter) and can be canceled by some aspectual operators. In particular, it can be canceled by the English progressive, as in (6b) and (7c), and by a delimitative operator, as in (7b). The delimitative operator is only compatible with some accomplishments, and its selectional restrictions vary from language to language. Thus, it is compatible with read the letter and not with open the door in English, but it is compatible with both in Balkar (see Section 2.3 below). Its overt realization also differs: it is silent in English and Balkar but may have an overt exponent in other languages, e.g., in Russian (the prefix po-). The meaning of this operator and its variable selectional restrictions are not addressed in this paper, but see Bar-el et al. (2005) and Tatevosov and Ivanov (2009) for different analyses.

1.3. Actuality Entailments

Let us now return to the three contrasts in Section 1.1: (a) some modal flavors trigger actuality entailments, while others do not (1); (b) actuality entailments arise in some aspectual contexts but not in others (2); (c) some modals trigger an anti-actuality entailment under negation, while others do not (3). These observations require further clarification before they can be sensibly accounted for. This clarification is precisely what this paper is set out to achieve.

First, which modal flavors have an actuality entailment, and which ones do not? The existing literature provides a variety of answers to this question. It is more or less generally acknowledged that actuality entailments do not arise with epistemic modals (Hacquard 2006, 2009, 2010). As for the root modality, there are various views. In particular, actuality entailments have been argued to be exclusively associated with ability implicatives (Bhatt 1999; Piñón 2003), all root modals (Hacquard 2006, 2009, 2010, 2014; Homer 2010), action-related dispositions (Mari and Martin 2007), teleological modals (Mari 2016), or causal modals (Nadathur 2019, 2020). In this paper, I provide preliminary evidence from Balkar that only causal modals can give rise to an actuality entailment (in particular, all universal and some existential causal modals), thus supporting the claims made by Nadathur (2019, 2020).

Second, which aspectual contexts trigger an actuality entailment, and which ones do not? As with the first question, the literature provides different answers. It has been argued that actuality entailments arise in all episodic aspectual contexts (Bhatt 1999), in all episodic contexts in the past tense (Piñón 2003), only in the context of the perfective aspect (Hacquard 2006, 2009, 2010, 2014; Mari 2016; Mari and Martin 2007; Nadathur 2019, 2020), and only in the context of the perfective aspect and a particular aspectual coercion operator (Homer 2010). In what follows, I provide preliminary evidence from Balkar that actuality entailments arise if and only if a causal modal has a telic interpretation, in other words, if it is not embedded under an imperfective or a delimitative operator, i.e., in exactly the same contexts in which (non-culminating) accomplishments give rise to a culmination entailment.

Third, which modals give rise to an anti-actuality entailment under negation, and which ones do not? Anti-actuality entailments have not been extensively studied before. In this paper, I provide preliminary evidence from Balkar that all existential causal modals (both those that have an actuality entailment and those that do not) give rise to an anti-actuality entailment under negation.

To sum up, this paper provides some preliminary evidence from Balkar for the following tentatively universal claims:

(8)	a.	Only causal modals can have actuality entailments (all universal ones and some existential ones).
	b.	Actuality entailments arise if and only if a causal modal is not embedded under an imperfective or a delimitative operator (whenever it has a telic interpretation).
	c.	Existential causal modals give rise to an anti-actuality entailment under negation.

In the second half of the paper, I develop Causal Modality Theory, which consists of two basic assumptions.

(9)	Causal Modality Theory (CMT):
	a.	Modals with causal flavor quantify over causal chains initiated by the counterparts of the anchor situation.
	b.	Some existential modals with causal flavor introduce a conditional presupposition: if some counterpart of the anchor situation caused another situation, then the anchor situation caused the same situation.

From (9a), it follows that the modal base of a causal modal operator includes the causal chain initiated by the anchor situation, because the counterpart relation is a reflexive relation (see Aloni 2001; Lewis 1968; Stalnaker 1987, and others). This explains (8c) and the part of (8a) that concerns universal modals.

From (9b), it follows that certain existential causal modals, namely, the ones with the conditional presupposition, trigger an actuality entailment in positive contexts. This explains the part of (8a) that concerns existential modals.

Under CMT, modals with an actuality entailment describe a complex situation consisting of two sub-situations: the anchor situation and a situation specified by the prejacent, which is a part of the causal chain initiated by the anchor situation. In other words, modals with an actuality entailment have the same semantics as accomplishments, that is, they are bi-eventive predicates; the causing situation is the anchor situation, and the caused situation is the situation described by the prejacent. The same semantics predicts the same behavior in the same aspectual contexts, which explains (8b).

Apart from providing an account of all the three generalizations in (8), CMT crucially treats the causal relation as a modal one (more precisely, as a type of accessibility relation; see Kratzer 1977, 1981, and subsequent work). This also has other benefits. First, it offers a unified view of culmination entailments of bi-eventive accomplishment predicates and actuality entailments of modals. Second, it provides a straightforward understanding of the ‘let’ vs. ‘make’ ambiguity of causative morphemes as an ambiguity in modal force (existential vs. universal), which also explains the behavior of causative morphemes in the scope of negation (‘not let’ ≈ ‘make not’). Third, it allows for a straightforward classification of the circumstantial and ability readings of root modals like the English can, the English have to, and the Balkar -al (‘can/may’) as different types of causal modality (see Section 5.1). All of them allow for counterfactual references in the terms of Lewis (1973) and Dowty (1979), and all of them can be paraphrased with ‘make’ (in the case of have to) or ‘let’ (in the case of can and -al (‘can/may’)).

The paper is organized as follows: In Section 2 below, I provide the background information about Balkar modal operators and accomplishments. In Section 3, Section 4 and Section 5, I consider several root modals in Balkar with deontic and causal flavors and argue for the three generalizations in (8). Section 6 lays out Causal Modality Theory.

2. Background

2.1. Preliminaries

In this section, I introduce four root modals and types of Aktionsart attested in Balkar. But before we proceed, I will give some basic information about Balkar verbal morphology and morphosyntax. Like other Turkic languages, Balkar has an SOV basic word order and a rich verbal morphology. The morphological template for a finite verb form is given in (10).

(10)	Root + Causative/Modal + Negation + Aspect/Tense + Agreement

This paper focuses on four modal elements: two suffixes and two lexical verbs. The two suffixes are the causative morpheme and the modal suffix -al with an existential ‘can/may’ reading, glossed as ‘poss’. Both suffixes have a fixed position in the verbal wordform. They follow the root and precede negation, as in (11). The modal suffix -al introduces its own (+back) domain for vowel harmony, which may be due to its historic relation to the light verb al (‘take’) in other Turkic languages (see, e.g., Grashchenkov 2015).

(11)	et-dir6-al-ma-dɨ
	do-caus-poss-neg-pst1
	‘(s)he couldn’t make him/her do something’

The two lexical verbs that are discussed in the paper are bujur (‘order’) and qoj (‘allow’). Both verbs take an infinitival clause as their complement (formed by a combination of the future-tense suffix and the dative case marker).

(12)	Fatima	sabij-le-ge2	[pro2	baxca-da	kitap	oqu-r-ʁa]	qoj-ʁan-dɨ
	Fatima	kid-pl-dat		garden-loc	book	read-fut-dat	allow-pst2-3
	‘Fatima allowed the children to read a book in the garden.’

Both verbs take three arguments: the subject (the one who orders/allows), the addressee (the one who is allowed/ordered to do something), and the prejacent (the infinitival clause). With the verb qoj (‘allow’), the addressee argument receives either dative or accusative.7

(13)	Fatima	{	Alim-ni2	/	Alim-ge2	}	[pro2	kitap	oqu-r-ʁa]	qoj-ʁan-dɨ
	Fatima		Alim-acc		Alim-dat			book	read-fut-dat	allow-pst2-3
	‘Fatima allowed Alim to read a book.’

With the verb bujur (‘order’), the addressee argument can only receive dative.

(14)	Fatima	{	*Alim-ni2	/	Alim-ge2	}	[pro2	kitap	oqu-r-ʁa]	bujur-ʁan-dɨ
	Fatima		Alim-acc		Alim-dat			book	read-fut-dat	order-pst2-3
	‘Fatima ordered Alim to read a book.’

In what follows, I assume that the infinitival clause has pro as its subject, which is obligatorily controlled by the addressee argument.

The prejacent of the causative suffix and of the suffix -al is a verb phrase, while the prejacent of the verbs bujur (‘order’) and qoj (‘allow’) is an infinitival clause (a tenseless TP).

2.2. Modality

Causatives introduce a new argument and a new subevent into the event and argument structure of the base verb (Harley 1996, 1997, 2008, 2011; Miyagawa 1998, 2012; Lyutikova et al. 2006; Ramchand 2008).

(15)	a.	Alim kitap oqu-du
		Alim book read-pst1
		‘Alim read a book.’
	b.	Madina [Alim-ge  kitap oqu]vP-t-du
		Madina Alim-dat book  read-caus-pst1
		‘Madina made Alim read a book.’

Causative constructions describe a complex situation consisting of two sub-situations: a situation introduced by a causative morpheme (Madina’s actions in (15b)) and a situation associated with the base verb (Alim’s actions in (15b)). In this paper, I treat the causative morpheme as a modal operator. The anchor situation is the causing situation. The prejacent is the base verb phrase that the causative morpheme takes as its complement.

There is a cross-linguistic distinction between so-called direct and so-called indirect causatives (see Comrie 1976; Harley 1996, 1997, 2008; Knecht 1986; Lyutikova et al. 2006; Miyagawa 1998, and many others). Direct causatives are formed from unaccusative verbs, while indirect ones are formed from unergative and transitive verbs. In this paper, I only consider indirect causatives.

Like causatives, constructions with qoj (‘allow’) and bujur (‘order’) describe complex situations consisting of two sub-situations: the situation associated with the modal verb (the teacher’s actions in (16a) and the principal’s actions in (16b)) and the situation associated with the infinitival clause (the children taking the teacher’s book in (16a) and the teachers looking through the notebooks in (16b)). These constructions also have modal semantics. The anchor situation is the situation associated with the modal verb and the prejacent is the infinitival clause.

(16)	a.	ustaz1    sabij-le-ge2  [pro2 kitab-ɨ1-n    al-ɨr-ʁa]TP     qoj-du
		teacher  kid-pl-dat             book-3-acc take-fut-dat allow-pst1
		‘The teacher1 allowed the children to  take their1 book.’
	b.	direktor   ustaz-la-ʁa2      [pro2  tetrad-la-ʁa           kara-r-ʁa]TP    bujur-du
		principal teacher-pl-dat             notebook-pl-dat look-fut-dat   order-pst1
		‘The principal ordered the teachers to look through the notebooks.’

The suffix -al has an existential modal meaning with various flavors. Clauses with -al also describe complex situations consisting of two sub-situations: the situation introduced by the suffix itself (the state of Alim’s physical abilities in (17)) and the situation associated with the base verb (Alim cutting down trees in (17)). The former is the anchor situation and the latter is the situation specified by the prejacent of -al (the verb phrase of the base verb).

(17)	[Alim terek-le-ni    au-dur]vP-al-a            edi
	Alim  tree-pl-acc   fall-caus-poss-conv  aux
	‘Alim was able to (was strong enough to) cut down trees.’

2.3. Aspect and Aktionsart

In this paper, I consider two viewpoint aspectual contexts: the past perfective (18a) and the episodic past imperfective (18b).

(18)	a.	men	kel-gen-de,	Kerim	aš	et-ken-di
		I	arrive-nzr-loc,	Kerim	food	make-pst2-3
		‘When I arrived, Kerim made food.’						arrive < make.food
	b.	men	kel-gen-de,	Kerim	aš	et-e	edi
		I	arrive-nzr-loc,	Kerim	food	make-conv	aux
		‘When I arrived, Kerim was making food.’						arrive ⊆ make.food

The past perfective is formed with -gan8 and introduces a time interval that includes the event time (see Klein 1994; Kratzer 1998a).9 The past imperfective is formed with the -j/-a converb10 and the auxiliary edi and introduces a time interval that is included in the event time (see Klein 1994; Kratzer 1998a). The past imperfective has both an episodic reading and a generic/habitual reading. In what follows, I only consider the episodic reading.

Based on the interpretations that verb phrases have under the two basic viewpoint aspects illustrated in (18), they can be split into classes, usually called Aktionsart (see Dowty 1979; Levin and Rappaport-Hovav 1995; Maslov 1948; Paducheva 2004; Vendler 1957; Tatevosov 2015, 2016, among many others). In this paper, I rely on the Aktionsart classification developed by Tatevosov (2015, 2016) and applied specifically to Balkar by Lyutikova et al. (2006).

Here and below, I primarily consider five classes of verb phrases attested in Balkar: accomplishments, non-culminating accomplishments, achievements, activities, and states. Their properties are summarized in (19).

(19)	Aktionsart in Balkar
	Class	Perfective		Episodic Imperfective
		Interpretation	Culmination	Interpretation	Culmination
	Accomplishments	Telic	Yes	Atelic	No
	Non-culminating	Telic	Yes	Atelic	No
	accomplishments	Atelic	No
	Achievements	Telic	Yes	– (Habitual only)
	Activities and states	Atelic	No	Atelic	No

The first class is accomplishments and, in Balkar, includes verbs al (‘take/buy’), kij (‘put.on’), sal (‘put’), cɨq (‘go.out’), and a few others (see Lyutikova et al. 2006, p. 267). Accomplishments only have a telic interpretation and give rise to a culmination entailment under the past perfective.

(20)	a.	Alim alma-nɨ     al-ʁan-dɨ
		Alim apple-acc take-pst2-3
		‘Alim took the apple.’
	b.	* Alim eki  minut   alma-nɨ     al-ʁan-dɨ
		Alim two minute apple-acc take-pst2-3
		Intended: ‘Alim tried to take the apple for two minutes (but didn’t take it).’
		Lit.: ‘Alim took the apple for two minutes.’

They are compatible with the episodic reading of the past imperfective, in which case they have an atelic interpretation and do not give rise to a culmination entailment.

(21)	Alim alma-nɨ     al-a            edi
	Alim apple-acc take-conv aux
	‘Alim was taking the apple (but didn’t take it).’

The second class is non-culminating accomplishments and, in Balkar, includes verbs ac (‘open’), kes (‘cut’), oqu (‘read’), et (‘do/make’), zaz (‘write’), and many others (see Lyutikova et al. 2006, p. 269). Non-culminating accomplishments have both a telic interpretation and an atelic interpretation under the past perfective. Only the telic interpretation gives rise to a culmination entailment.

(22)	a.	Fatima ešik-ni     ac-xan-dɨ
		Fatima door-acc open-pst2-3
		‘Fatima opened the door.’
	b.	Fatima eki   minut   ešik-ni     ac-xan-dɨ
		Fatima two minute door-acc open-pst2-3
		‘Fatima tried to open the door for two minutes (but didn’t open it).’
		Lit.: ‘Fatima opened the door for two minutes.’

The atelic interpretation can be characterized as a ‘failed attempt’ reading in the case of verbs like ac (‘open’) (the Agent tries to make the caused situation happen but eventually fails) or a ‘partial success’ reading in the case of verbs like zaz (‘write’) (the Agent initiates the caused situation but does not lead it to completion).

Non-culminating accomplishments have an atelic interpretation in the context of the episodic past imperfective and do not have a culmination entailment in this case.

(23)	Fatima eki   minut    ešik-ni     ac-a            edi
	Fatima two minute door-acc open-conv aux
	‘Fatima was opening the door for two minutes (but didn’t open it).’

In what follows, I assume that all Balkar accomplishments have a culmination entailment in their base meaning. This includes (a) verb phrases like alma-nɨ al (‘apple-acc take’), (b) verb phrases like ešik-ni ac (‘door-acc open’), and (c) verb phrases like kitap-nɨ oqu (‘book-acc read’). The delimitative operator is silent in Balkar and only compatible with accomplishments like (b) or (c) but not (a). In the case of (b) ešik-ni ac (‘door-acc open’), the delimitative operator leads to the ‘failed attempt’ reading, while in the case of (c) kitap-nɨ oqu, it can lead to either the ‘failed attempt’ or the ‘partial success’ reading; for more details see Tatevosov (2008) and Tatevosov and Ivanov (2009).

The third class is achievements and, in Balkar, consists of the verb tab (‘find’) (see Lyutikova et al. 2006, p. 268). Achievements only have a telic interpretation and give rise to a culmination entailment under the past perfective.

(24)	a.	Fatima kitap-nɨ    tap-xan-dɨ
		Fatima book-acc find-pst2-3
		‘Fatima found the book.’
	b.	* Fatima beš  minut   kitap-nɨ    tap-xan-dɨ
		Fatima five minute book-acc find-pst2-3
		Lit.: ‘Fatima found the book for five minutes.’

Unlike accomplishments, achievements are not compatible with the episodic reading of the past imperfective. In the context of an achievement verb phrase, the past imperfective only has a habitual interpretation, as in (25). In this case, achievements give rise to a ’habitually repeated’ culmination entailment.

(25)	Fatima kitap-nɨ    tab-a          edi
	Fatima book-acc find-conv aux
	1. ‘Fatima used to find the book (many times).’
	2. *‘Fatima was about to find the book (once).’

The fourth and fifth classes are activities and states. Activities in Balkar include the verbs saqla (‘wait’), izle (‘look.for’), sɨla (‘pet’), and a few others (see Lyutikova et al. 2006, p. 280), while states include the verb zaša (‘live’) and a couple of others (see Lyutikova et al. 2006, p. 285). Activities and states only have an atelic interpretation under the past perfective and have no culmination entailments.

(26)	a.	Fatima tefter-ni           eki  saʁat izle-gen-di
		Fatima notebook-acc two hour look.for-pst2-3
		‘Fatima looked for the notebook for two hours.’
	b.	* Fatima tefter-ni           eki   saʁat-xa   izle-gen-di11
		Fatima notebook-acc two hour-dat look.for-pst2-3
		Intended: ‘Fatima looked for the notebook and found it in two hours.’
		Lit.: ‘Fatima looked for the notebook in two hours.’

(27)	a.	Kerim eki   zɨl    Malqar-da     zaša-ʁan-dɨ
		Kerim two year Balkaria-loc live-pst2-3
		‘Kerim lived in Balkaria for two years.’
	b.	* Kerim eki   zɨl-ʁa       Malqar-da    zaša-ʁan-dɨ
		Kerim two year-dat Balkaria-loc live-pst2-3
		Lit.: ‘Kerim lived in Balkaria in two years.’

Activities and states are compatible with the episodic reading of the past imperfective, in which case they have the same atelic interpretation as with the past perfective.

(28)	Fatima tefter-ni           köp  izle-j                edi
	Fatima notebook-acc long look.for-conv aux
	‘Fatima was looking for a notebook for a long time.’

(29)	Kerim	Malqar-da	zaša-j	edi
	Kerim	Balkaria-loc	live-conv	aux
	‘Kerim lived in Balkaria.’

2.4. Outline

In Section 3, Section 4 and Section 5, I discuss the modal flavor, force, Aktionsart, and (anti-)actuality entailments of the causative morpheme, verbs bujur (‘order’) and qoj (‘allow’), and the suffix -al.

Section 3 shows that the causative suffix has fixed causal modal flavor (the anchor situation is related to the prejacent by causation) and variable force. The causative suffix is ambiguous between an existential ‘let’ reading and a universal ‘make’ reading. The argument introduced by the causative suffix can be either an Agent or a Causer. ‘Make’ causatives with an Agent behave like non-culminating accomplishments, namely, they can have both a telic reading and an atelic reading under the past perfective. They trigger an actuality entailment if and only if they have a telic interpretation. All the other readings of causative morphemes (‘make’ causatives with a causer and ‘let’ causatives) behave like accomplishments, that is, they only have a telic interpretation under the past perfective. They also trigger an actuality entailment whenever they have a telic interpretation (i.e., under the past perfective). Only existential causatives, but not universal ones, trigger an anti-actuality entailment under negation.

Section 4 is dedicated to the verbs bujur (‘order’) and qoj (‘allow’). Both verbs have deontic modal flavor; the verb qoj (‘allow’) is existential, while the verb bujur (‘order’) is universal. In addition, the verb qoj (‘allow’) can also have a causal interpretation (‘give an opportunity’). Deontic bujur (‘order’) and deontic qoj (‘allow’) behave like achievements with respect to Aktionsart, that is, they have a telic interpretation under the past perfective and are incompatible with the episodic reading of the past imperfective. Causal qoj (‘allow’) behaves like an accomplishment, that is, it is compatible with the episodic past imperfective and has an atelic interpretation in this case. The verb bujur (‘order’) triggers neither actuality nor anti-actuality entailments. Neither the deontic nor the causal flavor of qoj (‘allow’) gives rise to an actuality entailment, but the causal interpretation of qoj (‘allow’) triggers an anti-actuality entailment under negation.

Section 5 discusses the suffix -al (‘poss’). This suffix has an existential modal meaning with various flavors, including epistemic, deontic, circumstantial, and ability flavors. In Section 5.1, I argue that the latter two can be viewed as two sub-cases of a causal reading. Both readings can be straightforwardly classified as existential and causal, if one takes the modal view of causality, offered by CMT. Deontic -al behaves like a generic stative predicate, that is, it is incompatible with any of the episodic viewpoint aspects. Causal -al (including the circumstantial and ability readings) behaves like an accomplishment, that is, it has a telic interpretation under the past perfective and an atelic one under the episodic past imperfective. Only the causal interpretation of -al triggers an actuality entailment under the past perfective, and only the causal interpretation of -al triggers an anti-actuality entailment under negation.

(30)	Data summary
	Modal	Flavor	Force	Aktionsart	Actuality Entailments	Anti-Actuality Entailments
	‘Make’ causative Agent	Causal	□	(Non-culminating) accomplishment	Yes	No
	‘Make’ causative Causer	Causal	□	Accomplishment	Yes	No
	‘Let’ causative Agent/Causer	Causal	⋄	Accomplishment	Yes	Yes
	bujur (‘order’)	Deontic	□	Achievement	No	No
	qoj (‘allow’)	Deontic	⋄	Achievement	No	No
	qoj (‘allow’)	Causal	⋄	Accomplishment	No	Yes
	-al (‘poss’)	Deontic	⋄	Generic state	No	N/A (no)12
	-al (‘poss’)	Causal	⋄	Accomplishment	Yes	Yes

In sum, the paper describes three morphemes with a deontic modal meaning (bujur, deontic qoj, and deontic al) and four morphemes with a causal one (‘let’ causative, ‘make’ causative, causal qoj, and causal al) and provides preliminary empirical support for the three tentatively universal claims given in (8) and repeated in (31) below:

(31)	a.	Only causal modals can have actuality entailments (all universal ones and some existential ones).
	b.	Actuality entailments arise if and only if a causal modal is not embedded under an imperfective or a delimitative operator (whenever it has a telic interpretation).
	c.	Existential causal modals give rise to an anti-actuality entailment under negation.

3. Indirect Causatives

3.1. Flavors and Forces

Causative constructions describe a complex situation consisting of two sub-situations: a causing situation introduced by a causative morpheme and a caused situation specified by the base verb stem. The fact that these are two distinct situations becomes evident if we consider adverbial modification. For example, in (32a), the adverbial beš minut-xa (‘five minute-dat’) modifies the causing situation but not the caused one.13 Meanwhile, in (32b), it is the caused situation but not the causing one that is modified by the adverbial eki saʁat (‘two hour’).

(32)	a.	Fatima Alim-ge    beš minut-xa      it-ni        izle-t-gen-di
		Fatima Alim-dat five minute-dat dog-acc look.for-caus-pst2-3
		‘It took Fatima five minutes to make Alim look for the dog.’
	b.	Fatima Alim-ge   eki   saʁat it-ni        izle-t-gen-di
		Fatima Alim-dat two hour  dog-acc look.for-caus-pst2-3
		‘Fatima made it so that Alim looked for the dog for two hours.’

The descriptive properties of the causing situation and the theta role of the argument introduced by the causative morpheme are underspecified. The argument can be an Agent, as in (33a), or a Causer, as in (33b).

(33)	a.	Alim Fatima-ʁa    kitap-la-nɨ    ber-ip        adɨr-la-nɨ     stol-ʁa     sal-dɨr-ʁan-dɨ
		Alim Fatima-dat book-pl-acc give-conv dish-pl-acc table-dat put-caus-pst2-3
		‘Alim made Fatima put the dishes on the table (by) giving her books.’
	b.	it-ni        awru-u      Alim-ge   darman-la    al-dɨr-ʁan-dɨ
		dog-gen fall.sick-3 Alim-dat medicine-pl take-caus-pst2-3
		‘The dog’s sickness made Alim buy medicine.’

The causing situation can be agentive, as in (33a), which is a situation where Alim gives Fatima books, or not, as in (33b), which is a situation where the dog falls sick. Furthermore, it could also be a situation where an Agent does not do something and, as a result, brings about the caused situation, as in the case of the so-called ‘causation by omission’ reading (see Raffy 2021, pp. 14–18).

(34)	a.	Alim kel-me-j               üj        iš-i-n           Madina-ʁa    al-dɨr-ʁan-dɨ
		Alim arrive-neg-conv home work-3-acc Madina-dat take-caus-pst2-3
		‘Alim made Madina pick up his homework (by) not showing up.’
	b.	[Madina-nɨ   biz-ge   kitab-ɨ-n1    qajda  bux-tur-ʁan-ɨ-n
		Madina-gen 1pl-dat book-3-acc where hide-caus-nzr-3-acc
		ajt-ma-ʁan-ɨ]    biz-ge   a-nɨ1  köp  izle-t-gen-di
		say-neg-nzr-3 1pl-dat 3-acc long look.for-caus-pst2-3sg
		‘The fact that Madina didn’t tell us where she hid the book1 made us look for it1 for a long time.’

In (34a), Alim does not show up at school, and as a result, Madina has to pick up his homework for him; in other words, Alim makes Madina pick up his homework by not showing up. In (34b), Madina does not tell us where she hid the book, and as a result, we have to look for it for a long time; in other words, Madina makes us look for the book for a long time by not telling us where it is hidden.

The relation between the situation introduced by the causative morpheme and the situation specified by the base verb is causal. Causative constructions, like the one in (35), allow for a counterfactual inference (Dowty 1979; Lewis 1973). From (35), it follows that if Fatima had not called Kerim and told him to take the purse, he would not have taken it.

(35)	Fatima	Kerim-ge	söleš-ip	sumka=bla	axca-nɨ	al-dɨr-ʁan-dɨ
	Fatima	Kerim-dat	call-conv	purse=with	money-acc	take-caus-pst2-3
	‘Fatima called Kerim and made him take the purse with the money.’

The default reading of causative morphemes is universal (‘make’ reading), which is evident from the fact that (36a) is a contradiction, while (36b) is not. This means that ‘make’ causatives create a stronger modal statement than the causal reading of qoj. In particular, they introduce universal quantification over the same set of situations.

(36)	a.	[škol-nu      direktor-u]2 Madina-ʁa1  tefter-le-ni           oqu-t-xan-dɨ
		school-gen principal-3   Madina-dat notebook-pl-acc read-caus-pst2-3
		‘[The principal of the school]2 made Madina1 read the notebooks.’
		# alaj ol2   aŋa1    [pro1 tefter-le-ni            oqu-r-ʁa]        qoj-ma-ʁan-dɨ
		but 3sg 3sg.dat           notebook-pl-acc read-fut-dat allow-neg-pst2-3
		‘But he2 didn’t let her1 read the notebooks.’
	b.	[škol-nu     direktor-u]2 Madina-ʁa1   [pro1 tefter-le-ni            oqu-r-ʁa]        qoj-ʁan-dɨ
		school-gen principal-3   Madina-dat            notebook-pl-acc read-fut-dat allow-pst2-3
		‘[The principal of the school]2 let Madina1 read the notebooks.’
		alaj ol2  aŋa1      tefter-le-ni           oqu-t-ma-ʁan-dɨ
		but 3sg 3sg.dat notebook-pl-acc read-caus-neg-pst2-3
		‘But he2 didn’t make her1 read the notebooks.’

However, causative morphemes may also have an existential ‘let’ reading in the right context.

(37)	it-ni	zuqla-ʁan-ɨ	maŋa	tabaʁ-ɨ-n	al-dɨr-ʁan-dɨ
	dog-gen	sleep-nzr-3	1sg.dat	plate-3-acc	take-caus-pst2-3
	‘The fact that the dog was sleeping let me take its plate.’

In this context, the causative morpheme has a weaker reading: ‘let’ rather than ‘make’. Thus, both (38a) and (38b) are contradictions.

(38)	a.	it-ni         zuqla-ʁan-ɨ  maŋa    tabaʁ-ɨ-n     al-dɨr-ʁan-dɨ,
		dog-gen sleep-nzr-3 1sg.dat plate-3-acc take-caus-pst2-3
		# alaj al-ɨr-ʁa            qoj-ma-ʁan-dɨ
		but take-fut-dat allow-neg-pst2-3
		Lit.: ‘The fact that the dog was sleeping let, but didn’t allow me to take its plate.’
	b.	it-ni        zuqla-ʁan-ɨ  maŋa     tabaʁ-ɨ-n     al-ɨr-ʁa          qoj-ʁan-dɨ,
		dog-gen sleep-nzr-3 1sg.dat plate-3-acc take-fut-dat allow-pst2-3
		# alaj al-dɨr-ma-ʁan-dɨ
		but take-caus-neg-pst2-3
		Lit.: ‘The fact that the dog was sleeping allowed to, but didn’t let me take its plate.’

A potential analysis of these data can be that the base reading of the causative morpheme is weak (‘let’), but it can be strengthened pragmatically in sentences like (36). But a purely pragmatic approach would not work, because causative morphemes have both ‘make’ and ‘let’ readings in downward entailing environments. In fact, indirect causatives are known to be ambiguous under negation (see, e.g., Lyutikova et al. 2006, p. 132).

(39)	Fatima Kerim-ge    üj-nü         zɨj-dɨr-ma-ʁan-dɨ
	Fatima Kerim-dat home-acc clean-caus-neg-pst2-3
	1. ‘Fatima didn’t make Kerim clean the house (nothing happened/he did it himself).’
	2. ‘Fatima didn’t let Kerim clean the house.’

The second reading of (39) is usually described as negation taking scope below a causative morpheme (‘Fatima made Kerim not to clean the house’). But in view of the existence of examples like both (36) and (38), and the surface morpheme ordering in (39), namely, negation taking surface scope over a causative morpheme, (39) is probably also best analyzed as a causative being ambiguous between a universal ‘make’ reading and an existential ‘let’ reading under negation. Then, as expected, negation of the existential reading (the second interpretation of (39)) is truth-conditionally equivalent to the universal reading taking scope above negation: ¬∃x: $\varphi$↔∀x: $\neg \varphi$. Thus, the ‘let’–‘make’ ambiguity receives straightforward treatment as an ambiguity in quantificational force, while the semantic interactions of causative morphemes and negation follow automatically.

The existential ‘let’ reading of causative morphemes also leaves the descriptive properties of the causing situation and the theta role of the new argument underspecified. As with the universal ‘make’ reading, the argument introduced by a causative morpheme can be an Agent, as in (40a), or a Causer, as in (40b-i) and (40b-ii).

(40)	a.	Kerim ešik-ni      ac-ɨp           Madina-nɨ   kuxnja-dan  cɨʁ-ar-ʁan-dɨ
		Kerim door-acc open-conv Madina-acc kitchen-abl go.out-caus-pst2-3
		‘Kerim let Madina leave the kitchen (by) opening the door.’
	b.	Madina bil-me-gen-lej             kes-i-n     üj-de          beg-it-ti.
		Madina know-neg-nzr-temp self-3-acc home-loc lock-caus-pst1
		‘Madina accidentally locked herself in the house.’
		i.  alaj kirit-ni          sɨn-ŋan-ɨ       Madina-nɨ    üj-den       cɨʁ-ar-dɨ
		but padlock-gen break-nzr-3 Madina-acc house-abl go.out-caus-pst1
		‘But the breaking of the padlock let Madina out.’
		ii.  alaj kirit       sɨn-ɨp           Madina-nɨ    üj-den       cɨʁ-ar-dɨ
		but padlock break-conv Madina-acc house-abl go.out-caus-pst1
		‘But the padlock let Madina out (by) breaking.’

As with the universal meaning, the causing situation can be agentive (40a) or not (40b). Like ‘make’ causatives, ‘let’ causatives may also have a ‘causation by omission’ reading, under which the causing situation is a situation where an Agent does not do something.

(41)	it      ür-me-j             maŋa     tabaʁ-ɨ-n     al-dɨr-ʁan-dɨ
	dog bark-neg-conv 1sg.dat plate-3-acc take-caus-pst2-3
	‘The dog let me take its plate (by) not barking (and behaving quietly).’

As with ‘make’ causatives, the relation between the situation introduced by a ‘let’ causative and the situation specified by the base verb is causal. ‘Let’ causatives also allow for a counterfactual inference. For example, from (42), it follows that if the teacher had not left, the kids would not have looked for the answers in her office.

(42)	ustaz     ket-ip         sabij-le-ge   soruu-la-ʁa        zuuap-nɨ      kabinet-i-n-de
	teacher leave-conv kid-pl-dat question-pl-dat answer-acc office-3-obl-loc
	izle-t-gen-di
	look.for-caus-pst2-3
	‘The teacher left and let the kids look for the answers to the questions in her office.’

To sum up, causative morphemes introduce a new argument with the theta role of an Agent or a Causer, and a new underspecified situation (including situations where something does not happen) that has a causal relation to the situation described by the base verb. They have both a universal ‘make’ reading and an existential ‘let’ reading. Thus, they are best described as modal operators with a causal accessibility relation and variable force.

3.2. Aktionsart and Entailments

In this section, I investigate the Aktionsart of the causing situation (the situation introduced by a causative morpheme) to the exclusion of the situation specified by the base verb. In other words, I only discuss the Aktionsart of the causative morpheme itself.

3.2.1. Causatives with an Agent

Let us begin ‘make’-causatives with an Agent. Some ‘make’ causatives with an Agent only have a telic interpretation under the past perfective:

(43)	a.	Kerim beš  minut-xa      Alim-ge  kitap-nɨ    izle-t-gen-di
		Kerim five minute-dat Alim-dat book-acc look.for-caus-pst2-3
		‘Kerim made Alim look for the book in five minutes (it took Kerim five minutes to make Alim look for the book).’
	b.	? Kerim beš  minut   Fatima-ʁa   kitap tap-tɨr-ʁan-dɨ
		Kerim five minute Fatima-dat book find-caus-pst2-3
		1. *‘Kerim tried to make Fatima find a book for five minutes (but didn’t succeed).’
		2. ‘It took Kerim five minutes to make Fatima find a book.’

The telic adverbial beš minut-xa (‘five minute-dat’) in (43a) modifies the causative morpheme and not the base verb, because the base verb izle (‘look.for’) is an activity and cannot be modified by telic adverbials (see (26) in Section 2.3). Since (43a) is acceptable, it shows that the causative morpheme itself (to the exclusion of the base verb) can have a telic interpretation.

The atelic adverbial beš minut (‘five minute’) in (43b) cannot modify the base verb tap (‘find’), because it is an achievement and cannot be modified by atelic adverbials (see (24) in Section 2.3). As a result, the only way in which (43b) can have an acceptable interpretation is with beš minut (‘five minute’) modifying the causative morpheme. To the extent to which this sentence is acceptable, however, it can only have a telic interpretation (‘it took Kerim five minutes to make Fatima find a book’).14

However, a broader sample of indirect causatives studied by Lyutikova et al. (2006, pp. 352–61) reveals that most ‘make’ causatives with an Agent do have an atelic interpretation under the perfective, in addition to a telic one.

(44)	a.	ustaz    eki   minut-xa      alim-ni    cap-tɨr-dɨ
		teacher two minute-dat Alim-acc run-caus-pst1
		‘In two minutes, the teacher made Alim run (it took the teacher two minutes to make Alim run).’
	b.	ustaz     eki  minut    alim-ni    cap-tɨr-dɨ
		teacher two minute Alim-acc run-caus-pst1
		‘For two minutes, the teacher made Alim run (for two minutes the teacher was trying to make Alim run, but didn’t succeed).’   (Lyutikova et al. 2006, p. 359)

Which is the property that distinguishes between causatives like the one in (43b) and the one in (44b) remains beyond the scope of this paper.15 What is important for us here is that most ‘make’ causatives with an Agent behave like non-culminating accomplishments (see Section 1.2 and Section 2.3), in that they allow both a telic interpretation and an atelic interpretation under the past perfective. Notice that the atelic interpretation in (44b) can be characterized as a ‘failed attempt’ reading in the terminology of Tatevosov (2008) and Tatevosov and Ivanov (2009).

‘Make’ causatives with an Agent are compatible with the episodic past imperfective and have an atelic interpretation in this case.

(45)	Fatima	Alim-ge	kitap	oqu-t-a	edi
	Fatima	Alim-dat	book	read-caus-conv	aux
	‘Fatima was making Alim read a book.’

If a ‘make’ causative has a telic interpretation in the context of the past perfective (highlighted by a telic temporal adverbial like beš minut-xa (‘five minute-dat’)), it gives rise to an actuality entailment. The sentence in (46) entails that the caused situation took place in the actual world (the proposed continuation sounds contradictory).

(46)	Kerim beš  minut-xa      Alim-ge1 kitap-nɨ   izle-t-gen-di
	Kerim five minute-dat Alim-dat book-acc look.for-caus-pst2-3
	‘Kerim made Alim1 look for the book in five minutes.’
	# alaj ol1  izle-me-gen-di
	but 3sg look.for-neg-pst2-3
	‘But he1 didn’t.’

If a ‘make’ causative has an atelic interpretation in the context of the past perfective (highlighted by an atelic temporal adverbial like eki minut (‘two minute’)), it does not give rise to an actuality entailment. The sentence in (44b), repeated below, does not entail that the caused situation took place in the actual world:

(47)	ustaz     eki  minut   alim-ni     cap-tɨr-dɨ
	teacher two minute Alim-acc run-caus-pst1
	‘The teacher made Alim run for two minutes (for two minutes the teacher was trying to make Alim run, but didn’t succeed).’    (Lyutikova et al. 2006, p. 359)

In the context of the episodic past imperfective, the actuality entailment is canceled. The sentence in (48) does not entail that the caused situation took place in the actual world, and the proposed continuation does not sound contradictory.

(48)	Fatima Alim-ge1  kitap oqu-t-a               edi
	Fatima Alim-dat book read-caus-conv aux
	‘Fatima was making Alim1 read a book.’
	alaj ol1  kitap-nɨ    oqu-ma-j          edi
	but 3sg book-acc read-neg-conv aux
	‘But he1 wasn’t reading the book.’

Under negation, ‘make’ causatives with an Agent do not lead to an anti-actuality entailment. The sentence in (49) does not entail that the caused situation did not take place in the actual world and can be felicitously continued by ‘but he did’.

(49)	Alim-nɨ1   ata-sɨ     a-nɨ1  baxca-da     išle-t-me-gen-di
	Alim-gen father-3 3-acc garden-loc work-caus-neg-pst2-3
	‘Alim1’s father didn’t make him1 work in the garden.’
	alaj ol1  kesi baxca-da     išle-gen-di
	but 3sg self  garden-loc work-pst2-3
	‘But he1 worked in the garden by himself.’

To sum up, (most) ‘make’ causatives with an Agent behave like non-culminating accomplishments. They have both a telic interpretation and an atelic interpretation under the past perfective and an atelic interpretation in the context of the episodic past imperfective. They give rise to an actuality entailment in the same context in which non-culminating accomplishments give rise to a culmination entailment: whenever they have a telic interpretation (which is only possible under the past perfective and if there is no delimitative operator). ‘Make’ causatives with an Agent do not trigger an anti-actuality entailment under negation.

Let us now turn to ‘let’ causatives with an Agent. Unlike ‘make’ causatives with an Agent, ‘let’ causatives with an Agent only allow for a telic interpretation under the past perfective (50). This seems to be true for any ‘let’ causative with an Agent, regardless of the prejacent (see Lyutikova et al. 2006, p. 361, for a large and representative sample of verbs).

(50)	a.	Alim Fatima-nɨ     aš    et-gen        zer-den    cɨʁ-ar-ʁan-dɨ
		Alim Fatima-acc food make-nzr room-abl go.out-caus-pst2-3
		‘Alim let Fatima out of the kitchen.’
	b.	* Alim beš  minut   Fatima-nɨ    aš      et-gen       zer-den    cɨʁ-ar-ʁan-dɨ
		Alim five minute Fatima-acc food make-nzr room-abl go.out-caus-pst2-3
		Intended: ‘Alim tried to let Fatima out of the kitchen for five minutes (but didn’t succeed).’
		Lit.: ‘For five minutes, Alim let Fatima out of the kitchen.’

The atelic adverbial beš minut (‘five minutes’) in (50b) is not compatible with the main verb, ciʁ, because it is an accomplishment (see Section 2.3). As a result, the only way in which (50b) can be acceptable is if beš minut (‘five minutes’) modifies the ‘let’ causative. Since the sentence is ungrammatical with beš minut (‘five minutes’) but acceptable without it (50a), I conclude that ‘let’ causatives with an Agent do not have an atelic interpretation under the past perfective, but they do have a telic one.

‘Let’ causatives with an Agent are also compatible with the episodic past imperfective and have an atelic interpretation in this case.

(51)	Alim	Fatima-nɨ	aš	et-gen	zer-den	cɨʁ-ar-a	edi
	Alim	Fatima-acc	food	make-nzr	room-abl	go.out-caus-conv	aux
	‘Alim was letting Fatima out of the kitchen.’

In the context of the past perfective, ‘let’ causatives with an Agent invariably give rise to an actuality entailment. The first sentence in (52) entails that the caused situation took place in the actual world (hence, the proposed continuation sounds contradictory).

(52)	Alim Fatima-nɨ1   aš     et-gen       zer-den    cɨʁ-ar-ʁan-dɨ
	Alim Fatima-acc food make-nzr room-abl go.out-caus-pst2-3
	‘Alim let Fatima1 out of the kitchen.‘
	# alaj ol1   cɨq-ma-ʁan-dɨ
	but 3sg go.out-neg-pst2-3
	‘But she1 didn’t go out.’

In the context of the episodic past imperfective, the actuality entailment is canceled. The sentence in (53) does not entail that the caused situation took place in the actual world; thus, the proposed continuation does not sound contradictory.

(53)	Alim Fatima-nɨ1  aš      et-gen       zer-den    cɨʁ-ar-a                   edi
	Alim Fatima-acc food make-nzr room-abl go.out-caus-conv aux
	‘Alim was letting Fatima1 out of the kitchen.’
	alaj ol1  cɨq-ma-ʁan-dɨ
	but 3sg go.out-neg-pst2-3
	‘But she1 didn’t go out.’

Under negation, ‘let’ causatives give rise to an anti-actuality entailment. The sentence in (54) entails that the caused situation did not take place in the actual world (Kerim did not work in the room) and cannot be felicitously continued by ‘but he did’.16

(54)	Fatima Kerim-ni1  otou-da     išle-t-me-gen-di
	Fatima Kerim-acc room-loc work-caus-neg-pst2-3
	‘Fatima didn’t let Kerim1 work in the room.’
	# alaj ol1 išle-gen-di
	but he work-pst2-3
	‘But he1 did.’

To sum up, ‘let’ causatives with an Agent behave like accomplishments. They only have a telic interpretation under the past perfective, and they have an atelic interpretation in the context of the episodic past imperfective. They give rise to an actuality entailment under the past perfective but not under the episodic past imperfective. They also trigger an anti-actuality entailment under negation.

3.2.2. Causatives with a Causer

‘Make’ causatives with a Causer only have a telic interpretation under the past perfective.

(55)	a.	azɨq küj-gen     ijis      biz-ni    aš     et-gen       otou-dan  cɨʁ-ar-ʁan-dɨ
		food burn-nzr smell 1pl-acc food make-nzr room-abl go.out-caus-pst2-3
		‘The smell of burning food made us leave the kitchen.’
	b.	* azɨq  küj-gen     ijis     beš minut   biz-ni     aš      et-gen      otou-dan  cɨʁ-ar-ʁan-dɨ
		food burn-nzr smell five minute 1pl-acc food make-nzr room-abl go.out-caus-pst2-3
		Intended: ‘For five minutes, it smelled of burning food and we felt like we had to leave the kitchen (but we didn’t).’
		Lit.: ‘For five minutes, the smell of burning food made us leave the kitchen.’

The atelic adverbial beš minut (‘five minutes’) in (55b) is not compatible with the main verb, ciʁ, because it is an accomplishment (see Section 2.3). Hence, the only way in which (55b) can be acceptable is if beš minut (‘five minutes’) modifies the ‘make’ causative morpheme itself. Since the sentence is ungrammatical with beš minut (‘five minutes’) but acceptable without it (55a), I conclude that ‘let’ causatives with an Agent do not have an atelic interpretation under the past perfective, but they do have a telic one.

This seems to be true regardless of the prejacent of the causative morpheme. All ‘make’ causatives with a Causer only have a telic interpretation under the past perfective (see Lyutikova et al. 2006, p. 360). The same is true for ‘let’ causatives with a Causer.

(56)	a.	it-ni        zuqla-ʁan-ɨ  maŋa    tabaʁ-ɨ-n     al-dɨr-ʁan-dɨ
		dog-gen sleep-nzr-3 1sg.dat plate-3-acc take-caus-pst2-3
		‘The dog’s sleeping let me take its plate.’
	b.	* it-ni         zuqla-ʁan-ɨ beš  minut   maŋa    tabaʁ-ɨ-n     al-dɨr-ʁan-dɨ
		dog-gen sleep-nzr-3 five minute 1sg.dat plate-3-acc take-caus-pst2-3
		Intended: ‘For five minutes, I tried to take the dog’s plate, while it was sleeping (but didn’t succeed).’
		Lit.: ‘For five minutes, the dog’s sleeping let me take its plate.’

Both ‘make’ and ‘let’ causatives with a Causer are compatible with the episodic past imperfective, in which case they have an atelic interpretation.

(57)	a.	zauun biz-ge    avtobus-nu saqla-t-a              edi
		rain     1pl-dat bus-acc       wait-caus-conv aux
		‘The rain was making us wait for the bus.’
	b.	it-ni        zuqla-ʁan-ɨ  maŋa    tabaʁ-ɨ-n     al-dɨr-a                edi
		dog-gen sleep-nzr-3 1sg.dat plate-3-acc take-caus-conv aux
		‘The dog’s sleeping was letting me take its plate.’

In the context of the past perfective both ‘make’ and ‘let’ causatives with a Causer give rise to an actuality entailment.

(58)	a.	it-ni        awru-u     Fatima-ʁa1  darman   al-dɨr-ʁan-dɨ
		dog-gen fall.sick-3 Fatima-dat medicine take-caus-pst2-3
		‘The dog’s sickness made Fatima1 buy medicine.’
		# alaj ol1  al-ma-ʁan-dɨ
		but 3sg take-neg-pst2-3
		‘But she1 didn’t.’
	b.	Fatima-nɨ     üj-de        bol-ma-ʁan-ɨ   maŋa    üj-ü-n-de            it-ni        izle-t-gen-di
		Fatima-gen home-loc be-neg-nzr-3 1sg.dat home-3-obl-loc dog-acc look.for-caus-pst2-3
		‘The fact that Fatima wasn’t at home let me look for the dog in her house.’
		# alaj men izle-me-gen-me
		but 1sg  look.for-neg-pst2-1sg
		‘But I didn’t.’

In the context of the episodic past imperfective, the actuality entailment is canceled.

(59)	a.	zauun biz-ge    avtobus-nu saqla-t-a               edi
		rain     1pl-dat bus               wait-caus-conv   aux
		‘The rain was making us wait for the bus.’
		alaj biz saqla-ma-ʁan-bɨz
		but 1pl wait-neg-pst2-1pl
		‘But we didn’t.’
	b.	it-ni        zuqla-ʁan-ɨ  maŋa    tabaʁ-ɨ-n      al-dɨr-a              edi
		dog-gen sleep-nzr-3 1sg.dat plate-3-acc take-caus-conv aux
		‘The dog’s sleeping was letting me take its plate.’
		alaj men al-ma-ʁan-ma
		but 1sg   take-neg-pst2-1sg
		‘But I didn’t.’

As in the case of causatives with an Agent, under negation, ‘let’ causatives but not ‘make’ causatives give rise to an anti-actuality entailment.

(60)	a.	it-ni        ür-gen-i      em  qap-xan-ɨ   maŋa    tabaʁ-ɨ-n     al-dɨr-ma-ʁan-dɨ
		dog-gen bark-nzr-3 and bite-nzr-3 1sg.dat plate-3-acc take-caus-neg-pst2-3
		‘The dog’s barking and biting didn’t let me take its plate.’
		# alaj men al-ʁan-ma
		but 1sg  take-pst2-1sg
		‘But I did.’
	b.	zauun biz-ge    avtobus-nu saqla-t-ma-ʁan-dɨ
		rain     1pl-dat bus-acc       wait-caus-neg-pst2-3
		‘The rain didn’t make us wait for the bus.’
		alaj biz avtobus-nu saqla-ʁan-bɨz
		but 1pl bus-acc      wait-pst2-1pl
		‘But we did.’

To sum up, both ‘make’ and ‘let’ causatives with a Causer behave like accomplishments. They have a telic interpretation under the past perfective and an atelic interpretation under the episodic past imperfective. They give rise to an actuality entailment in the same contexts in which accomplishments give rise to a culmination entailment (under the past perfective). Only ‘let’ causatives with a Causer trigger an anti-actuality entailment under negation.

3.3. Interim Summary

Causative morphemes in Balkar can be analyzed as modal operators with a causal accessibility relation and variable force. That is, causative morphemes are ambiguous between an existential ‘let’ reading and a universal ‘make’ reading. The theta role of the argument and the descriptive properties of the situation introduced by the causative suffix are underspecified.

Universal causatives with an Agent behave like non-culminating accomplishments, in that they allow for both telic and atelic readings under the past perfective. All the other causatives (universal causatives with a Causer and both types of existential causatives) behave like accomplishments, in that they only allow for a telic interpretation in the same context.

Causatives give rise to an actuality entailment in the same contexts in which (non-culminating) accomplishments give rise to a culmination entailment, namely, only in case they have a telic interpretation (which is only available under the past perfective and if no delimitative operator is involved).

Finally, under negation, the existential ‘let’ causative but not the universal ‘make’ causative triggers an anti-actuality entailment.

4. ‘Allow’ and ‘Order’

4.1. Flavors and Forces

The verb bujur (‘order’) has a deontic interpretation. Sentences with bujur describe a complex situation consisting of two sub-situations: a situation of an authority figure (the subject of bujur) issuing a rule (the anchor situation) and a situation specified by the prejacent where this rule is being followed. Both situations can be independently modified by manner adverbs. For example, in (61a), terk oquna (‘quickly’) modifies the anchor situation (Fatima’s issuing of the order was quick). Meanwhile, in (61b), terk (‘quickly’) modifies the situation described by the prejacent (Alim’s running was supposed to be quick).

(61)	a.	Fatima terk       oquna Alim-ge1  [pro1 ešik-te          saqla-r-ʁa]      bujur-du
		Fatima quickly ptcl   Alim-dat            outside-loc wait-fut-dat order-pst1
		‘Fatima quickly ordered Alim to wait outside.’
	b.	Fatima Alim-ge1  [pro1 terk       cab-ar-ʁa]      bujur-du
		Fatima Alim-dat           quickly run-fut-dat order-pst1
		‘Fatima ordered Alim to run quickly.’

The verb qoj (‘allow’) also has a deontic interpretation. Sentences with qoj describe a complex situation consisting of two sub-situations: a situation of an authority figure (the subject of qoj) issuing a rule (the anchor situation)17 and a situation specified by the prejacent where this rule is being followed. Both situations can be independently modified by manner adverbs. For instance, in (62a) terk oquna (‘quickly’) modifies the anchor situation (Fatima’s issuing of the permission was quick). In (62b), terk (‘quickly’) modifies the situation described by the prejacent (Alim’s running was allowed to be quick).

(62)	a.	Fatima terk       oquna sabij-le-ge1  [pro1 ojna-r-ʁa]        qoj-du
		Fatima quickly ptcl   kid-pl-dat              play-fut-dat allow-pst1
		‘Fatima quickly allowed the kids to play (it didn’t take much time to convince her).’
	b.	Fatima Alim-ge1    [pro1 terk        cab-ar-ʁa]    qoj-du
		Fatima Alim-dat             quickly run-fut-dat allow-pst1
		‘Fatima allowed Alim to run quickly.’

The verb bujur (‘order’) has universal force and the verb qoj (‘allow’) has existential force, which is evident from the fact that (63a) is a contradiction, while (63b) is not. More precisely, the short text in (63a) implies that the teacher does not know their own mind, i.e., they are undecided as to whether to allow the kids to leave or not. Meanwhile, the short text in (63b) describes a perfectly consistent behavior of the same teacher: they allow the children to leave, but they do not require them to do so. Hence, bujur (‘order’) creates a stronger modal statement than qoj (‘allow’), in particular, bujur involves universal quantification, while qoj involves existential quantification over the same set of situations.

(63)	a.	ustaz2   sabij-le-ge1  [pro1 ket-er-ge]         bujur-du
		teacher kid-pl-dat             leave-fut-dat order-pst1
		‘The teacher2 ordered the kids1 to leave.’
		# alaj ol2  a-la-ʁa1   [pro1 ket-er-ge]         qoj-ma-d1
		but 3sg 3-pl-dat            leave-fut-dat allow-neg-pst1
		‘But they2 didn’t allow them1 to leave.’
	b.	ustaz2   sabij-le-ge1  [pro1 ket-er-ge]         qoj-du
		teacher kid-pl-dat             leave-fut-dat allow-pst1
		‘The teacher2 allowed the kids1 to leave.’
		alaj ol2  a-la-ʁa1  [pro1 ket-er-ge]         bujur-ma-dɨ
		but 3sg 3-pl-dat            leave-fut-dat order-neg-pst1
		‘But they2 didn’t order them1 to leave.’

The verb qoj (‘allow’) can have both an animate and an inanimate subject. In the latter case, illustrated by (64), the subject cannot be an authority figure, and qoj has causal flavor.

(64)	it-ni	zuqla-ʁan-ɨ	maŋa1	[pro1	tabaʁ-ɨ-n	al-ɨr-ʁa]	qoj-du
	dog-gen	sleep-nzr-3	1sg.dat		plate-3-acc	take-fut-dat	allow-pst1
	‘The dog’s sleeping gave me an opportunity to take its plate.’

Indeed, the sentence in (64) supports a counterfactual inference: if the dog had not been sleeping, I would not have taken its plate. Here, the verb qoj has the same meaning as the existential ‘let’ causative discussed in the previous section.

As with ‘let’ causatives, the subject’s theta role and the descriptive characteristics of the causing situation remain underspecified. In particular, the subject can be a Causer, as in (64), or an Agent, as in (65). This can be accounted for, if we assume that the deontic reading of qoj only allows for an animate agentive subject (the authority figure), while the causal reading of qoj, like the ‘let’ reading of causative morphemes, allows for both an inanimate non-agentive subject (as in (64)) and an animate agentive one (as in (65)). As a result, the string in (64) is unambiguously interpreted as causal, while the string in (65) is ambiguous between a causal reading (‘Kerim gave Madina the opportunity to … by opening the doors’) and a deontic reading (‘Kerlim allowed Madina to … after/while opening the doors’).

(65)	Kerim ešik-le-ni      ac-ɨp           Madina-nɨ1  [pro1 aš      üj-den
	Kerim door-pl-acc open-conv Madina-acc          food home-abl
	cɨʁ-ar-ʁa]           qoj-du
	go.out-fut-dat allow-pst1
	‘Kerim gave Madina an opportunity to go out of the kitchen by opening the doors.’

As with ‘let’ causatives, the causing situation can be a situation where an Agent does not do something and, as a result, brings about the caused situation (‘causation by omission’ reading).

(66)	[Fatima-nɨ   üj-de        bol-ma-ʁan-ɨ] maŋa1   [pro1 üj-ü-n-de              it-ni
	Fatima-gen home-loc be-neg-nzr-3  1sg.dat           home-3-obl-loc dog-acc
	izle-r-ge]              qoj-ʁan-dɨ
	look.for-fut-dat allow-pst2-3
	‘The fact that Fatima wasn’t home gave me an opportunity to look for the dog in her house.’

The causal reading of qoj is existential and not universal, as is evident from the contradiction in (67).

(67)	it-ni        awru-u      Alim-ge  darman-la    al-dɨr-ʁan-dɨ
	dog-gen fall.sick-3 Alim-dat medicine-pl take-caus-pst2-3
	‘The dog’s sickness made Alim buy medicine,…’
	# alaj qoj-ma-ʁan-dɨ
	but allow-neg-pst2-3
	‘…but didn’t let (him do it).’

4.2. Aktionsart and Entailments

As in Section 3.2 for causatives, in this section, I focus specifically on the Aktionsart of the anchor situation associated with the verbs bujur and qoj themselves to the exclusion of the situation described by their prejacent.

4.2.1. Deontic ‘Order’ and ‘Allow’

Deontic bujur (‘order’) and deontic qoj (‘allow’) are achievements. The verb bujur only has a telic interpretation under the past perfective.

(68)	a.	Fatima Alim-ge1   [pro1 alma  al-ɨr-ʁa]          bujur-ʁan-dɨ
		Fatima Alim-dat            apple take-fut-dat order-pst2-3
		‘Fatima ordered Alim to take an apple.’
	b.	? Fatima beš  minut     Alim-ge1   [pro1 alma  al-ɨr-ʁa]          bujur-ʁan-dɨ
		Fatima five minutes Alim-dat            apple take-fut-dat order-pst2-3
		1. *‘Fatima tried to order Alim to take an apple for five minutes (but didn’t succeed).’
		2. ‘It took Fatima five minutes to order Alim to take an apple.’

To the extent to which the sentence in (68b) is acceptable, it has a telic interpretation: ‘it took Fatima five minutes to order Alim to take an apple’.

The same is true for the deontic interpretation of qoj (‘allow’).

(69)	a.	ustaz    sabij-le-ge1  [pro1 kesi-ni   kitab-ɨ-n      al-ɨr-ʁa]          qoj-ʁan-dɨ
		teacher kid-pl-dat            self-gen book-3-acc take-fut-dat allow-pst2-3
		‘The teacher2 allowed the kids to take their2 book.’
	b.	ustaz    sabij-le-ge1  [pro1 kesi-ni   kitab-ɨ-n      al-ɨr-ʁa]          beš minut  qoj-ʁan-dɨ
		teacher kid-pl-dat            self-gen book-3-acc take-fut-dat five minute allow-pst2-3
		1. *‘The teacher2 tried to allow the kids to take their2 book for five minutes (but didn’t succeed).’
		2. ‘It took the teacher2 five minutes to allow the kids to take their2 book.’

Neither bujur (‘order’) nor deontic qoj (‘allow’) are compatible with the episodic past imperfective. In the context of these verbs, the past imperfective morphology can only have a habitual interpretation.

(70)	a.	Fatima	Kerim-ge1	[pro1	axca	al-ɨr-ʁa]	bujur-a	edi
		Fatima	Kerim-dat		money	take-fut-dat	order-conv	aux
		1. ‘Fatima used to order Kerim to take money (many times).’
		2. *‘Fatima was ordering Kerim to take money (once).’
	b.	ustaz	sabij-le-ge1	[pro1	kesi-ni	kitab-ɨ-n	al-ɨr-ʁa]	qoj-a	edi
		teacher	kid-pl-dat		self-gen	book-3-acc	take-fut-dat	allow-conv	aux
		1. ‘The teacher2 used to allow the kids to take their2 book (many times).’
		2. *‘The teacher2 was allowing the kids to take their2 book (once).’

Neither bujur (‘order’) nor deontic qoj (‘allow’) give rise to an actuality entailment under the perfective aspect. Neither (71a) nor (71b) entail that the prejacent situation took place in the actual world. Fatima can order Alim to take an apple without him taking it (71a), and a teacher can allow kids to take a book without them taking it (71b). Hence, the proposed continuations are felicitous and non-contradictory.

(71)	a.	Fatima Alim-ge1   [pro1 alma  al-ɨr-ʁa]          bujur-ʁan-dɨ
		Fatima Alim-dat            apple take-fut-dat order-pst2-3
		‘Fatima ordered Alim1 to take an apple.’
		alaj ol1  a-nɨ    al-ma-ʁan-dɨ
		but 3sg 3-acc take-neg-pst2-3
		‘But he1 didn’t.’
	b.	ustaz   sabij-le-ge1  [pro1 kesi-ni    kitab-ɨ-n      al-ɨr-ʁa]         qoj-ʁan-dɨ
		teacher kid-pl-dat            self-gen book-3-acc take-fut-dat allow-pst2-3
		‘The teacher2 allowed the kids1 to take their2 book.’
		alaj a-la1 al-ma-ʁan-dɨ-la
		but 3-pl  take-neg-pst2-3-pl
		‘But they1 didn’t.’

There is also no actuality entailment in the context of the habitual past imperfective.

(72)	a.	Fatima Kerim-ge1   [pro1 axca      al-ɨr-ʁa]         bujur-a        edi
		Fatima Kerim-dat            money take-fut-dat order-conv aux
		‘Fatima used to order Kerim1 to take money (many times).’
		alaj ol1  al-ma-j               edi
		but 3sg take-neg-conv aux
		‘But he1 didn’t.’
	b.	ustaz     sabij-le-ge1  [pro1 kesi-ni   kitab-ɨ-n      al-ɨr-ʁa]         qoj-a            edi
		teacher kid-pl-dat             self-gen book-3-acc take-fut-dat allow-conv aux
		‘The teacher2 used to allow the kids1 to take their2 book (many times).’
		alaj a-la1 al-ma-j               edi-le
		but 3-pl  take-neg-conv aux-pl
		‘But they1 didn’t.’

Neither deontic bujur (‘order’) nor deontic qoj (‘allow’) trigger an anti-actuality entailment under negation. Neither (73a) nor (73b) entail that the prejacent situation did not take place in the actual world. The first sentence in (73a) is true even if the kids actually played in the garden, and the first sentence in (73b) is true even if Alim actually cut down trees. Hence, the proposed continuations are non-contradictory.

(73)	a.	Fatima sabij-le-ge1 [pro1 baxca-da      ojna-r-ʁa]      qoj-ma-ʁan-dɨ
		Fatima kid-pl-dat            garden-loc play-fut-dat allow-neg-pst2-3
		‘Fatima didn’t allow the kids1 to play in the garden.’
		alaj a-la1 ojna-ʁan-dɨ-la
		but 3-pl  play-pst2-3-pl
		‘But they1 did.’
	b.	Kerim Alim-ge1 [pro1 terek-le-ni    tuura-r-ʁa]  bujur-ma-ʁan-dɨ
		Kerim Alim-dat           tree-pl-acc cut-fut-dat order-neg-pst2-3
		‘Kerim didn’t order Alim1 to cut down trees.’
		alaj ol1  tuura-ʁan-dɨ
		but 3sg cut-pst2-3
		‘But he1 did.’

4.2.2. Causal ‘Allow’

Causal qoj (‘allow’) is an accomplishment. It only has a telic interpretation under the past perfective.

(74)	a.	it-ni         zuqla-ʁan-ɨ  maŋa1   [pro1 tabaʁ-ɨ-n     al-ɨr-ʁa]         qoj-ʁan-dɨ
		dog-gen sleep-nzr-3 1sg.dat            plate-3-acc take-fut-dat allow-pst2-3
		‘The dog’s sleeping gave me an opportunity to take its plate.’
	b.	* it-ni         zuqla-ʁan-ɨ  maŋa1 [pro1 tabaʁ-ɨ-n      al-ɨr-ʁa]         beš minut    qoj-ʁan-dɨ
		dog-gen sleep-nzr-3 1sg.dat          plate-3-acc take-fut-dat five minute allow-pst2-3
		Lit.: ‘For five minutes, the dog’s sleeping gave me an opportunity to take its plate.’

Importantly, the telic interpretation in cases like (74a) should be attributed to the modal and not to its prejacent. The reason is that the telic interpretation arises even in cases when the prejacent is an activity and may not have telic readings. For example, in (75), the telic adverbial beš minut-xa (‘five minute-dat’) can only modify the modal and not the prejacent, because the verb s1la (‘pet’) is an activity (see Lyutikova et al. 2006, p. 280).

(75)	it      maŋa1  beš minut-xa       [pro1            sɨla-r-ʁa]       qoj-ʁan-dɨ
	dog 1sg.dat five minute-dat pet-fut-dat allow-pst2-3
	‘In five minutes, the dog gave me an opportunity to pet it (it took five minutes for the dog to get used to me enough to let me pet it).’

Unlike deontic qoj, causal qoj is compatible with the episodic past imperfective and has an atelic interpretation in this case.

(76)	it-ni        zuqla-ʁan-ɨ  maŋa1   [pro1 tabaʁ-ɨ-n     al-ɨr-ʁa]         qoj-a             edi
	dog-gen sleep-nzr-3 1sg.dat           plate-3-acc take-fut-dat allow-conv aux
	‘The dog’s sleeping was giving me an opportunity to take its plate.’

Causal qoj triggers no actuality entailments, neither in the context of the past perfective nor in the context of the episodic past imperfective.

(77)	a.	it-ni        zuqla-ʁan-ɨ  maŋa1   [pro1 tabaʁ-ɨ-n     al-ɨr-ʁa]         qoj-ʁan-dɨ
		dog-gen sleep-nzr-3 1sg.dat           plate-3-acc take-fut-dat allow-pst2-3
		‘The dog’s sleeping gave me an opportunity to take its plate.’
		alaj men tabaʁ-ɨ-n     al-ma-ʁan-ma
		but 1sg   plate-3-acc take-neg-pst2-1sg
		‘But I didn’t.’
	b.	it-ni        zuqla-ʁan-ɨ  maŋa1   [pro1 tabaʁ-ɨ-n     al-ɨr-ʁa]         qoj-a             edi
		dog-gen sleep-nzr-3 1sg.dat           plate-3-acc take-fut-dat allow-conv aux
		‘The dog’s sleeping was giving me an opportunity to take its plate.’
		alaj men tabaʁ-ɨ-n     al-ma-ʁan-ma
		but 1sg   plate-3-acc take-neg-pst2-1sg
		‘But I didn’t.’

However, causal ‘allow’ does trigger an anti-actuality entailment under negation. The first sentence in (78) entails that Fatima did not read the book.

(78)	awru-u     Fatima-ʁa1  [pro1 kitap-nɨ     oqu-r-ʁa]       qoj-ma-ʁan-dɨ
	fall.sick-3 Fatima-dat            book-acc read-fut-dat allow-neg-pst2-3
	‘The sickness didn’t give Fatima1 an opportunity to read the book.’
	# alaj ol1  oqu-ʁan-dɨ
	but 3sg read-pst2-3
	‘But she1 did.’

4.3. Interim Summary

The verbs bujur (‘order’) and qoj (‘allow’) are modal operators with a deontic accessibility relation. In addition, qoj (‘allow’) may have a causal interpretation.

Deontic bujur (‘order’) and deontic qoj (‘allow’) are achievements, that is, they have a telic interpretation under the past perfective and are incompatible with the episodic past imperfective. Causal qoj (‘allow’), however, behaves like an accomplishment. It has a telic interpretation under the past perfective and an atelic one under the episodic past imperfective.

Neither qoj (‘allow’) nor bujur (‘order’) gives rise to an actuality entailment (under any reading). But causal qoj (‘allow’) gives rise to an anti-actuality entailment under negation.

5. Possibility

5.1. Flavors and Forces

The suffix -al is an existential modal operator compatible with various accessibility relations. In particular, it can have an epistemic reading (79a), a deontic reading (79b), a circumstantial reading (79c), and an ability reading (79d).

(79)	a.	ol    bu  kitap-nɨ    da    ol    kitap-nɨ    da   al-al-a                 edi
		3sg this book-acc add that book-acc add take-poss-conv aux
		‘(I don’t know) He may have bought this book and he may have bought that book.’
	b.	ustaz-nɨ        ajt-xan-ɨ-na     köre    sabij-le škol-ʁa        kel-al-a                  edi-le
		teacher-gen say-nzr-3-dat as.per kid-pl   school-dat arrive-poss-conv aux-pl
		‘By the teacher’s permission, the kids were allowed to come to school.’
	c.	otou-da     zarɨq  bol-ʁan-ɨ ücün      men kitap oqu-jal-a            edi-m
		room-loc bright be-nzr-3 because 1sg   book read-poss-conv aux-1sg
		‘Because it was bright in the room, I was able to read a book.’
	d.	zarau      et-ip       tur-ʁan-ɨ      ücün      Madina auur    girja-la-nɨ        kütür-al-a        edi
		training do-conv stand-nzr-3 because Madina heavy weight-pl-acc lift-poss-conv aux
		‘Because of her training, Madina was able to lift heavy weights.’

For the purposes of this paper, I only focus on the root readings of -al, i.e., deontic, circumstantial, and ability, as in (79b)–(79d). Under all of them, -al introduces a new situation into the event structure of the base verb, namely, the anchor situation. In (79b), it is a situation of a rule being in place. In (79c), it is a situation of the room being bright. In (79d), it is a situation of Madina having certain physical abilities. The prejacent of -al is a verb phrase.

The situation introduced by -al is crucially distinct from the situation described by its prejacent, which is evident from the consistent ambiguity of event modifiers with -al. For example, in (80), the adverbial bir saʁat (‘one hour’) can either modify the anchor situation (the rule was in place for one hour) or the situation described by the verb phrase in the complement of -al (the writing of this letter was allowed to last for one hour).

(80)	Alim kaʁɨt-nɨ     bir  saʁat zaz-al-a               edi
	Alim letter-acc one hour write-poss-conv aux
	1. ‘It was allowed for Alim to write this letter for an hour.’
	2. ‘It was allowed for an hour for Alim to write this letter.’

In (81a), the adverb terk (‘quick’) modifies the prejacent situation, not the anchor situation (my entering the house was quick). In (81b), the adverbial kün zar1m (‘day half’) modifies the anchor situation, not the prejacent situation (the possibility for me to read a book, i.e., the situation of it being bright in the room, lasted half a day).

(81)	a.	ešik   ac-ɨl-ip                bol-ʁan-ɨ  ücün      men üj-ge         terk    kir-al-dɨ-m
		door open-pass-conv be-pst2-3 because 1sg   home-dat quick enter-poss-pst1-1sg
		‘Because the door was open, I could enter the house quickly.’
	b.	otou-da    zarɨq   bol-ʁan-ɨ ücün      men kün zarɨm kitap oqu-jal-a             edi-m
		room-loc bright be-nzr-3 because 1sg   day  half    book read-poss-conv aux-1sg
		‘Because it was bright in the room, for half a day I could read a book.’

In (82), the temporal clause Alim žaš zaman1nda (‘when Alim was young’) modifies the anchor situation introduced by -al; it temporally locates the situation of Alim having certain physical abilities. Meanwhile, the adverb terk (‘quick’) modifies the complement of -al, not -al itself. It is Alim’s running that was quick, not his having certain physical abilities.

(82)	Alim	žaš	zaman-ɨ-n-da	terk	cab-al-a	edi
	Alim	young	time-3-obl-loc	quick	run-poss-conv	aux
	‘When Alim was young, he could run quickly.’

The circumstantial and the ability readings in (79c) and (79d), respectively, are usually analyzed as two different accessibility relations. But they can both be viewed as causal. Both sentences in (79c) and (79d) support a counterfactual inference. From (79c), it follows that if it had not been bright enough in the room, I would not have read a book; from (79d), it follows that if Fatima had not had certain physical abilities, she would not have lifted heavy weights. Thus, under the broad counterfactual view of the causative relation, dating back to Lewis (1973) and Dowty (1979), the circumstantial reading in (79c) and the ability reading in (79d) involve the causal relation. Furthermore, treating the causal relation as a modal one allows us to identify the causal readings in (79c) and (79d) as nothing more than instances of an existential causal modal, akin to the ‘let’ reading of causative morphemes. Indeed, both (79c) and (79d) are easily paraphrasable with ‘let’ or ‘allow’: ‘the brightness of the room {let me/allowed me to} read a book’; ‘Madina’s training {let her/allowed her to} lift heavy weights’.

In what follows, I assume that -al is compatible with two root accessibility relations: a deontic one, as in (79b), and a causal one, as in (79c)–(79d).

5.2. Aktionsart and Entailments

Crucially, in this section, I consider the Aktionsart of the suffix -al itself to the exclusion of its complement verb phrase.

5.2.1. Deontic Possibility

Deontic -al behaves like a stative verb with a fixed generic interpretation.18 Unlike other stative verbs in Balkar (see Section 2.3), it is incompatible with the past perfective. Thus, the sentence in (83) only has a causal reading (the children managed to come to school), but not a deontic one (the children were allowed to come to school).

(83)	ustaz-nɨ	ajt-xan-ɨ-na	köre	sabij-le	škol-ʁa	kel-al-ʁan-dɨ-la
	teacher-gen	say-nzr-3-dat	as.per	kid-pl	school-dat	arrive-poss-pst2-3-pl
	1. ‘According to the teacher’s report, the children were able to come to school.’
	2. *‘By the teacher’s permission, the children were allowed to come to school.’

Deontic -al is not compatible with the episodic reading of the past imperfective either. In the context of the past imperfective morphology, -al describes a state of affairs that is neither episodic nor habitual but rather generic.

(84)	zaŋɨ	zakon-la=bla	Fatima	eki	zagranpasport	al-al-a	edi
	new	law-pl=with	Fatima	two	foreign.passport	take-poss-conv	aux
	‘By the new laws, Fatima could receive two passports for travel.’

In the only aspectual context in which it is attested (the generic past imperfective), deontic -al triggers no actuality entailment. The sentence in (84) does not entail that Fatima did receive two passports for travel.

(85)	zaŋɨ	zakon-la=bla	Fatima	eki	zagranpasport	al-al-a	edi
	new	law-pl=with	Fatima	two	foreign.passport	take-poss-conv	aux
	‘By the new laws, Fatima could receive two passports for travel.’
	alaj	al-ma-dɨ
	but	take-neg-pst1
	‘But she didn’t.’

Deontic -al is also not compatible with negation. Only the causal reading is available in this context, as shown in (86a). To express the lack of deontic ability, the speakers use a different modal operator, zaramajdɨ (‘forbidden’), as in (86b).19

(86)	a.	zoruq-la-ʁa köre   sabij-le škol-da       ojna-jal-ma-j              edi-le
		rule-pl-dat as.per kid-pl  school-loc play-poss-neg-conv aux-pl
		1. ‘The children were not able to play at school in accordance with the rules.’
		2. *‘By the rules, the children were forbidden to play at school.’
	b.	zoruq-la-ʁa köre   sabij-le-ge1  [pro1 škol-da       ojna-r-ʁa]      zaramajdɨ
		rule-pl-dat as.per kid-pl-dat            school-loc play-fut-dat forbidden
		‘By the rules, the children were forbidden to play at school.’

As a result, it is impossible to test whether the deontic reading of -al triggers an anti-actuality entailment under negation. But, at least, its negative counterpart, zaramajdɨ (‘forbidden’), does not. The sentence in (87) does not entail that the children did not play at school.

(87)	zoruq-la-ʁa köre    sabij-le-ge1 [pro1 škol-da       ojna-r-ʁa]       zaramajdɨ
	rule-pl-dat as.per kid-pl-dat            school-loc play-fut-dat forbidden
	‘By the rules, the children were forbidden to play at school.’
	alaj a-la  škol-da      ojna-j         edi-le
	but 3-pl school-loc play-conv aux-pl
	‘But they did.’

5.2.2. Causal Possibility

Unlike deontic -al, causal -al is an accomplishment. It has a telic interpretation under the past perfective.

(88)	a.	Axmat arba-nɨ   eki  saʁat-xa   türt-al-ʁan-dɨ
		Axmat cart-acc two hour-dat push-poss-pst2-3
		‘Axmat was able to push the cart in two hours.’
	b.	kün-nü   ariu bol-ʁan-ɨ ücün       biz  (*beš saʁat) tau-da              zol-nu
		day-gen nice be-nzr-3  because 1pl  five    hour  mountain-loc road-acc
		tab-al-ʁan-bɨz
		find-poss-pst2-1pl
		‘Due to the nice weather, we were able to find the road in the mountains (for five hours).’

Crucially, in (88a), the telic adverbial eki saʁat-xa (‘two hour-dat’) cannot modify the base verb türt (‘push’), because this verb is an activity and is incompatible with telic adverbials (see Lyutikova et al. 2006, p. 280). Hence, eki saʁat-xa (‘two hour-dat’) must modify the modal suffix -al (‘be able to’) itself, which means that this suffix has a genuine telic interpretation under the past perfective that is not due to its prejacent but rather to the suffix itself.

The sentence in (88b) cannot be modified by the atelic adverbial beš saʁat (‘five hours’) (an addition of the adverbial leads to ungrammaticality). The base verb tap (‘find’) cannot be modified by atelic adverbials because it is an achievement (see Section 2.3). Thus, if beš saʁat (‘five hours’) were acceptable in (88b), it would only be due to the suffix -al. Since modification by this adverbial is not acceptable, we have to conclude that causal -al does not have an atelic reading in this context.

Causal -al is compatible with the episodic past imperfective and has an atelic interpretation in this case.

(89)	otou-da	zarɨq	bol-ʁan-ɨ	ücün	men	kitap	oqu-jal-a	edi-m
	room-loc	bright	be-nzr-3	because	1sg	book	read-poss-conv	aux-1sg
	‘Because it was bright in the room, I was able to read a book.’

Thus, under a causal reading, in the context of the past perfective, the modal suffix -al is compatible with telic adverbials like ‘in two hours’ and incompatible with atelic ones like ‘for five hours’. At the same time, it is compatible with the episodic reading of the past imperfective. This makes this suffix an accomplishment (as per definitions in Section 2.3).

Causal -al triggers an actuality entailment under the past perfective. The sentence in (90) entails that the prejacent of -al is true in the actual world; hence, the proposed continuation sounds contradictory.

(90)	otou-da    zarɨq   bol-ʁan-ɨ ücün     men kitap oqu-jal-ʁan-ma
	room-loc bright be-nzr-3 because 1sg  book read-poss-pst2-1sg
	‘Because it was bright in the room, I was able to read a book.’
	# alaj men oqu-ʁan-ma
	but 1sg  read-pst2-1sg
	‘But I didn’t.’

In the context of the episodic past imperfective, the actuality entailment is canceled. The sentence in (91) does not entail that a prejacent situation took place in the actual world and can be felicitously continued by ‘but I didn’t’.

(91)	otou-da    zarɨq   bol-ʁan-ɨ ücün      men kitap oqu-jal-a            edi-m
	room-loc bright be-nzr-3 because 1sg   book read-poss-conv aux-1sg
	‘Because it was bright in the room, I was able to read a book.’
	alaj men oqu-ʁan-ma
	but   1sg               read-pst2-1sg
	‘But I didn’t.’

Under negation, causal -al gives rise to an anti-actuality entailment. The sentence in (92) entails that Fatima did not go to the city and cannot be felicitously continued by ‘but she went’.

(92)	awru-ʁan-1       sebepli Fatima šaxar-ʁa bar-al-ma-dɨ
	fall.sick-pst2-3 due.to   Fatima city-dat go-poss-neg-pst1
	‘Due to her sickness, Fatima wasn’t able to go to the city.’
	# alaj ol    bar-dɨ
	but 3sg go-pst1
	‘But she went.’

5.3. Interim Summary

To sum up, the suffix -al is an existential modal operator that can take various accessibility relations, including deontic and causal ones.

Deontic -al behaves like a generic stative predicate. It is not compatible with episodic aspectual contexts and does not trigger either actuality or anti-actuality entailments.

Causal -al behaves like an accomplishment. It has a telic interpretation under the past perfective and an atelic interpretation under the episodic past imperfective. Whenever it has a telic interpretation, causal -al gives rise to an actuality entailment. Under negation, it triggers an anti-actuality entailment.

6. Analysis

6.1. Root Modals in Balkar

In this paper, I discussed several root modal operators in Balkar with deontic and causal flavors. They can be split into three classes. First, there are causal modals, which trigger an actuality entailment and, if existential, give rise to an anti-actuality entailment under negation. This class includes ‘let’ and ‘make’ causatives, and causal -al. Second, there is an existential causal modal, qoj, that triggers no actuality entailment but gives rise to an anti-actuality entailment under negation. Third, there are deontic modals bujur, qoj, and -al, which trigger no actuality entailments and no anti-actuality entailments.

(93)	Summary (see (30))
	Modal	Flavor	Force	Aktionsart	Actuality Entailments	Anti-Actuality Entailments
	‘Make’ causative Agent	Causal	□	(Non-culminating) Accomplishment	Yes	No
	‘Make’ causative Causer	Causal	□	Accomplishment	Yes	No
	‘Let’ causative Agent/Causer	Causal	⋄	Accomplishment	Yes	Yes
	-al (‘poss’)	Causal	⋄	Accomplishment	Yes	Yes
	qoj (‘allow’)	Causal	⋄	Accomplishment	No	Yes
	bujur (‘order’)	Deontic	□	Achievement	No	No
	qoj (‘allow’)	Deontic	⋄	Achievement	No	No
	-al (‘poss’)	Deontic	⋄	Generic state	No	N/A (no)

Those causal modals that do give rise to an actuality entailment do so only if they receive a telic interpretation. In other words, they only trigger an actuality entailment if they are not embedded under an imperfective or a delimitative operator, that is, in the same contexts in which (non-culminating) accomplishments give rise to a culmination entailment.

This case study provides evidence for the three tentative claims stated at the beginning of the paper:

(94)	a.	Only causal modals can have actuality entailments (all universal ones and some existential ones).
	b.	Actuality entailments arise if and only if a causal modal is not embedded under an imperfective or a delimitative operator (whenever it has a telic interpretation).
	c.	Existential causal modals give rise to an anti-actuality entailment under negation.

In this section, I offer a theory of deontic and causal modality within the framework of situation semantics that accounts for these three claims. The proposed theory of causal modality consists of two core assumptions.

(95)	Causal Modality Theory:
	a.	Modals with causal flavor quantify over causal chains initiated by the counterparts of the anchor situation.
	b.	Some existential modals with causal flavor introduce a conditional presupposition: if some counterpart of the anchor situation caused another situation, then the anchor situation caused the same situation.

In what follows, Section 6.2 introduces basic concepts in situation semantics and defines all the notions related to causation that are necessary to formulate the proposed theory of causal modality. Section 6.3 provides the proposed lexical entries for all the deontic and causal modals discussed in this paper.

6.2. Situation Semantics and Causation

6.2.1. Situation Semantics

In this paper, I adopt the framework of situation semantics introduced by Barwise (1981) and Barwise and Perry (1983) and developed by Bach (1986), Kratzer (1989, 1998b, 2002, 2007), Portner (1992), von Fintel (1994), and Moulton (2015), among many others. This section introduces and describes core notions from this framework that are used below to formulate the proposed theory of deontic and causal root modality.

In situation semantics, a situation is usually understood as a slice of a possible world, consisting of a set of individuals and some but not necessarily all their properties (see Kratzer 1998b, 2002, 2007). The domain of situations is abbreviated as D_s. Propositions are predicates over situations (type <st>). Alternatively, a situation can be understood as a piece of information about a set of individuals in a given possible world (see, e.g., Devlin 2006; Ginzburg and Sag 2000).

For example, the situation in (96) includes three teapots and a table, and nothing else. There are four individuals in this situation and three properties: three individuals are teapots, and one individual is a table; the three teapot individuals are standing on the table individual. Crucially, this situation does not include any other individuals, like Rosa, Karl, the floor, etc. Furthermore, this situation does not include any other properties, like the three teapots being seen by Rosa, the three teapots belonging to Karl, the three teapots being round, etc.20

(96)	Three teapots on a table

Situations can be summed by the ‘⊕’ operator and can stand in a part–whole relation written as ‘⪯’ and formally defined in (97) below (see Link 1998, p. 17). For example, a situation that includes the table and two out of the three teapots in (96) is a sub-situation or a part of the situation in (96).

(97)	∀s1,s2∈Ds: s1⪯ s2 if and only if s1⊕ s2 = s2.

A possible world can be defined as a maximal situation (see Bach 1986; Portner 1992).

(98)	w is a possible world if and only if w∈Ds and ¬∃s∈Ds: w ⪯ s and w ≠ s.

One and the same situation cannot be part of two possible worlds; in other words, possible worlds ’do not intersect’. As a result, for each situation s in D_s, there is one and only one world that contains it, abbreviated as w_s. This principle is stated more formally in (99):

(99)	a.	∀w,w${}^{\prime }$∈Ds: (w, w${}^{\prime }$ are possible worlds and w ≠ w${}^{\prime }$) → (¬∃s: s ⪯ w and s ⪯ w${}^{\prime }$).
	b.	∀s: ws is the only possible world w such that s ⪯ w.

Propositions are functions from situations to truth values, or characteristic functions of sets of situations. For example, the proposition in (100) is true in the situation in (96).

(100)

p = $\lambda$s. There are three teapots on a table in s.

The proposition in (100) is not only true in the situation in (96) but also in all the situations that include it. For example, proposition (100) is true in a situation that includes not only the three teapots and the table in (100) but also Rosa looking at them. This proposition is not true, however, in a sub-situation of the situation in (96) that includes only two out of the three teapots.

There is an exemplification relation between propositions and situations, defined as follows (see Kratzer 1998b, 2002, 2007):

(101)

A situation s exemplifies a proposition p if either s is the minimal situation in which p is true or p is true in all sub-situations of s.21

Whenever quantification over situations is involved, it is restricted by contextual factors, including topic–focus articulation and presuppositions (see, e.g., von Fintel 1994, 2004). For example, the set of situations that exemplify the proposition in (102), which corresponds to the sentence there are no teapots, includes a lot of situations that are not at all similar to each other (for instance, a situation where I scratch my nose). If the predicate in (102) is closed by an existential quantifier over situations as a part of the truth conditions of a sentence in the natural language, this quantifier is restricted to the Topic Situations, e.g., the situations that take place in the room in which the speaker is located at the moment.

(102)

p = $\lambda$s. ¬∃x: x is a teapot in s.

In what follows, I analyze verb phrases (and extended verbal projections like TPs) as predicates over situations with the semantic type <st>.

6.2.2. Causal Dependency

Before discussing the lexical entries for deontic and causal modal operators, I will define the notion of causal dependency, which relies on counterfactual inferences (see Dowty 1979; Lewis 1973, and others). This notion is used in the theory of causal modality and causation in Section 6.3, in particular in formulating the meanings of ‘let’ and ‘make’ causatives. In this section, I do not discuss the difference between ‘let’ and ‘make’ but rather the more basic relation of causal dependency between two situations, which is made use of in both ‘let’ meanings and ‘make’ meanings.

The notion of causal dependency relies on the notion of counterpart relation (see Aloni 2001; Lewis 1968; Stalnaker 1987, and others). Intuitively, a counterpart of an individual x in a world w is another individual x${}^{\prime }$ in another world w${}^{\prime }$ that shares some fundamental properties with x. Importantly, the counterpart relation is a reflexive relation, that is, every individual in every world is a counterpart of itself.

(103)

If w and w${}^{\prime }$ are possible worlds, x ⪯ w, and x${}^{\prime }$⪯ w${}^{\prime }$, then C(x)(x${}^{\prime }$) means that x${}^{\prime }$ is the counterpart of x in w${}^{\prime }$.

For example, a counterpart of Rosa Luxemburg in another world could be a female political thinker whose name is Rosa Luxemburg, but unlike in our world, she could be born in Switzerland. The question of which properties are fundamental and which ones are not remains beyond the scope of this paper (for more discussion, see Aloni 2001; Stalnaker 1987, among others).

A counterpart of a situation s in a world w is another situation s${}^{\prime }$ in another world w${}^{\prime }$ which, by assumption, is identical to s. For the purposes of the counterpart relation between situations, identity is understood as follows:

(104)

∀s,s${}^{\prime }$∈Ds: C(s)(s${}^{\prime }$) if and only if s${}^{\prime }$ includes the counterparts of all the individuals in s and no other individuals, and all the same properties as s and no other properties and has the same temporal coordinates as s.

For example, a counterpart of the situation in (96) is another situation in another possible world that has the same temporal coordinates and includes the counterparts of the three teapots and the table (and no other individuals) and the information about the three teapots being teapots, the table being a table, and the teapots being on the table (and no other information).

Two possible worlds can be identical to each other, ‘modulo situations s₁…s_n’, which means that these worlds are identical in all respects except that for every situation s₁…s_n, one of the worlds contains it, while the other one has no counterpart of it.

(105)	w ${\simeq }_{s_1...s_n}$ w${}^{\prime }$ if and only if w and w${}^{\prime }$ are identical in all respects except that for all s in {s1…sn} one of the following applies:
	a. s ⪯ w and ¬∃s${}^{\prime }$⪯w${}^{\prime }$: C(s)(s${}^{\prime }$);
	b. s ⪯ w${}^{\prime }$ and ¬∃s${}^{\prime }$⪯w: C(s)(s${}^{\prime }$).

We can now define the relation of causal dependency between two situations based on a counterfactual inference (see Lewis 1973, 2000; Dowty 1979). Situation s₂ is causally dependent on situation s₁, abbreviated as C-Dep(s₁)(s₂), if and only if both s₁ and s₂ are part of the same world w and, in every world w′ that is identical to w ‘modulo s₁ and s₂’ and in which there is no counterpart of s₁, there is also no counterpart of s₂.

(106)	C-Dep(s1)(s2) if and only if the following apply:
	a. ws1 = ws2 = w;	(s1 and s2 are part of the same world w)
	b. ∀w${}^{\prime }$: [w ${\simeq }_{s_1,s_2}$ w${}^{\prime }$ and ¬∃s1${}^{\prime }$∈w${}^{\prime }$: C(s1)(s1${}^{\prime }$)] → [¬∃s2${}^{\prime }$∈w${}^{\prime }$: C(s2)(s2${}^{\prime }$)].

Let us consider the following two examples:

(107)	a. Rosa made Karl enter the building.
	b. Rosa let Karl enter the building.

Both sentences describe two situations (one with Rosa and one with Karl) with one being causally dependent on the other. The difference between make and let has to do with modal force and is addressed below in Section 6.3. For the purposes of this section, I only focus on the notion of causal dependency, which applies to both make and let.

Both sentences have a ‘causation by action’ reading and a ‘causation by omission’ reading. Under the ‘causation by action’ reading, Rosa does something, which makes or lets Karl enter the building. Under the ‘causation by omission’ reading, Rosa does not do something, which makes or lets Karl enter the building.

Under the ‘causation by action’ reading, the sentence in (107a) is true if, for example, Rosa drags Karl into the building. In this case, there is a situation (s₁) in our world w that includes Rosa, Karl, and the building and exemplifies p = λs. Rosa drags Karl into the building in s. There is also a situation (s₂) in our world w that includes Karl and the building and exemplifies q = λs. Karl enters the building in s. Situation s₂ is causally dependent on situation s₁, that is, in all the worlds w${}^{\prime }$ identical to our world w ‘modulo s₁ and s₂’ where there is no counterpart of s₁ (no situation that includes Rosa, Karl, and the building; that takes place at the same time; and where Rosa drags Karl into the building), there is also no counterpart of s₂ (no situation that includes Karl and the building, that takes place at the same time, and where Karl enters the building). In other words, if Rosa had not dragged Karl into the building, he would not have entered it.

Under the same ‘causation by action’ reading, the sentence in (107b) is true if, for example, Rosa works in the building and uses her ID card to open the door and lets Karl in. In this case, there is a situation (s₁) in our world w that includes Rosa, her ID card, and the building door and exemplifies p = λs. Rosa uses her ID card to open the building door in s. There is also a situation (s₂) in our world w that includes Karl and the building and exemplifies q = λs. Karl enters the building in s. Situation s₂ is causally dependent on situation s₁, that is, in all the worlds w${}^{\prime }$ identical to our world w ‘modulo s₁ and s₂’ where there is no counterpart of s₁ (no situation that includes Rosa, her ID card, and the door; that takes place at the same time; and where Rosa uses her ID card to open the door), there is also no counterpart of s₂ (no situation that includes Karl and the building, that takes place at the same time, and where Karl enters the building). In other words, if Rosa had not used her ID card to open the building door, Karl would not have entered the building.

Under the ‘causation by omission’ reading, the sentence in (107a) is true if, for example, Karl wants to give Rosa some papers, so he comes to the building where Rosa works. He does not want to go inside the building, but he knows that Rosa will not go out (perhaps because she is too busy working). As a result, Karl is forced to enter. In other words, Rosa makes Karl enter the building by not going out. In this case, there is a situation (s₁) in our world w that includes Rosa, Karl, and the building and exemplifies p = λs. Rosa does not go out of the building to meet Karl in s. There is also a situation (s₂) in our world w that includes Karl and the building and exemplifies q = λs. Karl enters the building in s. Situation s₂ is causally dependent on situation s₁, that is, in all the worlds w${}^{\prime }$ identical to our world w ‘modulo s₁ and s₂’ where there is no counterpart of s₁ (no situation that includes Rosa, the building, and Karl; that takes place at the same time; and where Rosa does not go out to meet Karl), there is also no counterpart of s₂ (no situation that includes Karl and the building, takes place at the same time, and where Karl enters the building). In other words, if Rosa had gone out to meet Karl, he would not have entered the building.

Finally, under the same ‘causation by omission’ reading, the sentence in (107b) is true if, for example, Karl wants to enter the building, but Rosa can prevent him from doing so by locking the door. Nevertheless, she does not lock the door, and Karl enters the building. In this case, there is a situation (s₁) in our world w that includes Rosa and the door and exemplifies p = λs. Rosa does not lock the building door in s. There is also a situation (s₂) in our world w that includes Karl and the building and exemplifies q = λs. Karl enters the building in s. Situation s₂ is causally dependent on situation s₁, that is, in all the worlds w${}^{\prime }$ identical to our world w ‘modulo s₁ and s₂’ where there is no counterpart of s₁ (no situation that includes Rosa and the door, that takes place at the same time, and where Rosa does not lock the door), there is also no counterpart of s₂ (no situation that includes Karl and the building, that takes place at the same time, and where Karl enters the building). In other worlds, if Rosa had locked the door, Karl would not have entered the building.

The final notion that is needed for causal modality is the notion of causal chain (see Dowty 1979, pp. 104–7). Every situation s₀ initiates a causal chain, which is another situation s that is a sum of a set of situations (s = s₀⊕s₁⊕…⊕s_n), abbreviated as C-Chain(s₀). The causal chain of s₀ is the maximal ordered set of situations starting with s₀ where each next situation is causally dependent on the previous one.22

(108)	C-Chain(s0) is a situation s = s0⊕s1⊕…⊕sn such that the following apply:
	a. ∀i,j: (0≤i≤n and 0≤j≤n and j = i + 1) → C-Dep(si)(sj);
	b. n is the maximal number for which (a) is true.

By the definition of causal dependency in (106), for situation s₂ to be causally dependent on situation s₁, s₁ and s₂ must be part of the same world. Since the causal chain of a situation includes a series of situations causally dependent on each other (see (108)), it follows that for any situation s, its causal chain C-Chain(s) is part of the same world as s.

(109)	Causal Chain Theorem
	∀s∈Ds: C-Chain(s) ⪯ ws.

6.3. Modal Operators

6.3.1. Aspectual Operators and Semantic Composition

In this section, I discuss the assumed meanings of the prejacents of deontic and causal modals and the assumed meanings of the viewpoint aspect morphology.

The root modals discussed in this paper take two types of complements (prejacents): a verb phrase (as in the case of causative morphemes and -al) or a tenseless TP (as in the case of bujur and qoj). These two types of prejacents are illustrated in (110):

(110)	a.	it-ni        zuqla-ʁan-ɨ  maŋa1    [pro1 tabaʁ-ɨ-n     al-ɨr-ʁa]TP      qoj-du
		dog-gen sleep-nzr-3 1sg.dat            plate-3-acc take-fut-dat allow-pst1
		‘The dog’s sleeping gave me an opportunity to take its plate.’
	b.	it-ni        zuqla-ʁan-ɨ  [maŋa   tabaʁ-ɨ-n     al]vP-dɨr-ʁan-dɨ
		dog-gen sleep-nzr-3 1sg.dat plate-3-acc take-caus-pst2-3
		‘The dog’s sleeping let me take its plate.’

In what follows, I assume that the prejacents of all root modals in Balkar have the semantic type <st> (a predicate over situations or a proposition). The meanings for the prejacents in (110) are given in (111):

(111)	a.	$\left[\right[$ [pro1 take it2’s plate’]TP${\left]\right]}^{w,g}$ = $\lambda$s. g(1) takes g(2)’s plate in s.
	b.	$\left[\right[$ [I take it2’s plate]vP${\left]\right]}^{w,g}$ = $\lambda$s. the speaker takes g(2)’s plate in s.

These predicates are not restricted to minimal situations. For instance, the predicate over situations in (111b) is true for any situation in which the speaker takes g(2)’s plate, which could include other things, e.g., g(2) sitting quietly and not barking.

As for the viewpoint aspect, I assume that the Asp head also takes a predicate of situations as its complement. Following Dowty (1979), Parsons (1990), and Landman (1992), among others, I assume that some aspectual operators, like the past perfective, entail that a complete situation described by their complement takes place in the world of evaluation. Meanwhile, other aspectual operators, like the episodic imperfective or the delimitative operator, entail that a part of a situation described by their complement takes place in the world of evaluation.

The Asp head introduces the Topic Situation, which corresponds to Klein’s (1994) Topic Time; see also Kratzer (1998a). The assumed meanings of the perfective and the episodic imperfective are given below:

(112)	a.	$\left[\right[$pfv${\left]\right]}^{w,g}$ = $\lambda$p. $\lambda$s. s⪯w and ∃s${}^{\prime }$: p(s${}^{\prime }$) and s${}^{\prime }$⪯s and $\tau$(s${}^{\prime }$) ⊆$\tau$(s).
	b.	$\left[\right[$imp${\left]\right]}^{w,g}$ = $\lambda$p. $\lambda$s. s⪯w and ∃s${}^{\prime }$,w${}^{\prime }$: p(s${}^{\prime }$) and <s${}^{\prime }$,w${}^{\prime }$> ∈ CON(s)(w).
	In the above, $\tau$(s) is the temporal coordinate of s (the runtime of s), and CON(s)(w) is a continuation branch of situation s in w (based on Landman 1992, pp. 26–28).

The Topic Situation (variable s in (112)) takes place in the world of evaluation. As for the situation described by the complement of Asp (variable s′ in (112)), this depends on the Asp head.

In the case of the perfective (112a), the situation described by the complement of Asp is a sub-situation of the Topic Situation and is temporally included in it. Since the Topic Situation is part of evaluation world w, it follows that the situation described by the complement of Asp is also part of evaluation world w (by the transitivity of the part–whole relation; see Link 1998 and Section 6.2.1 above). Hence, perfective clauses entail that a whole situation described by their verb phrase takes place in their world of evaluation.

In the case of the episodic imperfective (112b), the situation described by the complement of Asp is on a continuation branch of the Topic Situation. This entails that the Topic Situation, which takes place in the world of evaluation, is a stage of the situation described by the complement of Asp, which does not necessarily take place in the world of evaluation (see Landman 1992). In other words, in this case, only a part of the situation described by the complement of Asp takes place in the world of evaluation.

Importantly, if situation s initiates a causal chain, it does not follow that any sub-situation or any stage of s initiates the same causal chain. In other words, if only a part of s takes place in the world of evaluation, it does not necessarily initiate the same chain of situations as the whole s would.

Let us take, for example, the following meaning of an accomplishment verb phrase:

(113)

$\left[\right[$ [Rosa cross the street]vP${\left]\right]}^{w,g}$ = $\lambda$s. Rosa is going across the street in s, and Rosa is on the other side of the street in C-Chain(s).

The verb phrase in (113) describes a situation (s) in which Rosa is going across the street and which initiates a causal chain (C-Chain(s)). Rosa is on the other side of the street in C-Chain(s) but not in s itself.

If this verb phrase is embedded under the perfective (112a), s takes place in the world of evaluation. As a result, by the Causal Chain Theorem (109), C-Chain(s) also takes place in the world of evaluation (Rosa ends up on the other side of the street).

If this verb phrase is embedded under the episodic imperfective (112b), however, only a part of s takes place in the world of evaluation. The whole situation s initiates a causal chain where Rosa is on the other side of the street, but a part of s may not. Since the whole situation s does not necessarily take place in the world of evaluation, C-Chain(s) does not necessarily take place in the world of evaluation either. Hence, Rosa may or may not end up on the other side of the street.

In other words, if the situation described by the complement of Asp (s) initiates a causal chain, this causal chain takes place in the world of evaluation if s does (e.g., in the context of the perfective) but not necessarily so if only a part of s does (e.g., in the context of the episodic imperfective).

The delimitative operator has a meaning similar to that of the episodic imperfective in all the relevant respects, but it is attached below in the viewpoint aspect (see Bar-el et al. 2005; Tatevosov 2008; Tatevosov and Ivanov 2009).23 It is only compatible with some accomplishments; in particular, it is compatible with ‘make’ causatives with an Agent but not with any other causal modal. The question of why it has this particular selectional restriction remains beyond the scope of this paper; for some discussion on and an analysis of the cross-linguistic variation in the selectional restrictions of the delimitative operator, see Tatevosov (2008) and Tatevosov and Ivanov (2009).

6.3.2. Deontic Modality

In this section, I provide the proposed lexical entries for deontic modal operators in Balkar. There are three deontic modals that are discussed in this paper: bujur (‘order’) (universal), deontic qoj (‘allow’) (existential), and deontic -al (existential). None of them trigger either actuality or anti-actuality entailments.

(114)	Deontic modals in Balkar
	Modal	Flavor	Force	Aktionsart	Actuality Entailments	Anti-Actuality Entailments
	bujur (‘order’)	Deontic	□	Achievement	No	No
	qoj (‘allow’)	Deontic	⋄	Achievement	No	No
	-al (‘poss’)	Deontic	⋄	Generic state	No	N/A (no)

A deontic modal introduces a situation that involves a particular rule or a particular law and quantifies over situations where this rule or law is being followed. Two deontic accessibility relations are defined in (115).24

(115)	a.	For any individuals x and y, and situations s and s${}^{\prime }$, Deon(x)(y)(s)(s${}^{\prime }$) if and only if the following apply:
		i.	s is a situation of x issuing a rule to y;
		ii.	s${}^{\prime }$ is a situation where this rule is being followed.
	b.	For any individual x, and situations s and s${}^{\prime }$, Deon(x)(s)(s${}^{\prime }$) if and only if the following apply:
		i.	s is a situation of some rule being in place that concerns x;
		ii.	s${}^{\prime }$ is a situation where this rule is being followed.

The verbs bujur (‘order’) and qoj (‘allow’) use the deontic accessibility relation in (115a), while deontic -al uses the deontic accessibility relation in (115b):

(116)	a.	$\left[\right[$ bujur□,deon${\left]\right]}^{w,g}$ = $\lambda$p. $\lambda$x. $\lambda$y. $\lambda$s. ∀s${}^{\prime }$: Deon(x)(y)(s)(s${}^{\prime }$) → p(s${}^{\prime }$).
	b.	$\left[\right[$ qoj⋄,deon${\left]\right]}^{w,g}$ = $\lambda$p. $\lambda$x. $\lambda$y. $\lambda$s. ∃s${}^{\prime }$: Deon(x)(y)(s)(s${}^{\prime }$) and p(s${}^{\prime }$).
	c.	$\left[\right[$ al⋄,deon${\left]\right]}^{w,g}$ = $\lambda$p. $\lambda$x. $\lambda$s. ∃s${}^{\prime }$: Deon(x)(s)(s${}^{\prime }$) and p(s${}^{\prime }$).

After the modals in (116) are fed their prejacent and their other arguments, the resulting meaning is a predicate over situations. In the case of deontic bujur, this predicate looks as follows:

(117)	a.	[ustaz2 sabij-le-ge1 [pro1 ket-er-ge]TP     bujur]ModP-du
		teacher kid-pl-dat           leave-fut-dat order-pst1
		‘The teacher2 ordered the kids1 to leave.’
	b.	$\left[\right[$ ModP ${\left]\right]}^{w,g}$ = $\lambda$s. ∀s${}^{\prime }$: Deon(the teacher)(the kids)(s)(s${}^{\prime }$) → the kids leave in s${}^{\prime }$.

The proposition in (117b) is true in a situation s if and only if s is a situation in which the teacher issues a rule to the kids (see (115a-i)) and, in every situation s′ in which this rule is being followed, the kids leave.

The meaning of ModP headed by deontic qoj is given in (118).

(118)	a.	[Fatima Alim-ge1 [pro1 terk       cab-ar-ʁa]TP  qoj]ModP-du
		Fatima  Alim-dat          quickly run-fut-dat  allow-pst1
		‘Fatima allowed Alim to run quickly.’
	b.	$\left[\right[$ ModP ${\left]\right]}^{w,g}$ = $\lambda$s. ∃s${}^{\prime }$: Deon(Alim)(Fatima)(s)(s${}^{\prime }$) and Alim runs quickly in s${}^{\prime }$.

The proposition in (118b) is true in a situation s if and only if s is a situation in which Fatima issues a rule to Alim (see (115a-i)) and there is another situation s′ where this rule is being followed, in which Alim runs (see (115a-ii)).

The meaning of ModP headed by deontic -al is given in (119).

(119)	a.	ustaz-nɨ	ajt-xan-ɨ-na	köre	[sabij-le	[škol-ʁa	kel]vP-al]ModP-a	edi-le
		teacher-gen	say-nzr-3-dat	as.per	kid-pl	school-dat	arrive-poss-conv	aux-pl
		‘By the teacher’s permission, the kids were allowed to come to school.’
	b.	$\left[\right[$ ModP ${\left]\right]}^{w,g}$ = $\lambda$s. ∃s${}^{\prime }$: Deon(the kids)(s)(s${}^{\prime }$) and the kids come to school in s${}^{\prime }$.

The proposition in (119b) is true in a situation s if and only if s is a situation in which there is some rule being in place that concerns the kids (115b-i)25 and there is another situation s′ where this rule is being followed, in which the kids come to school (115b-ii).

It is easy to see that under the proposed analysis, deontic modals do not trigger actuality entailments. The situations that they quantify over do not take place in the world of evaluation. They are simply situations that follow a particular rule that is issued or is in place in the world of evaluation. Only the anchor situation, i.e., the situation of someone issuing the rule or the situation of the rule being in place, takes place in the world of evaluation. Depending on the aspect morphology, either the whole of the anchor situation or its part takes place in the world of evaluation (see Section 6.3.1 and Bach 1986; Bennett and Partee 1972; Dowty 1979; Klein 1994; Landman 1992; Parsons 1990, among many others).

It is also expected that they do not trigger anti-actuality entailments. Negation applies to the existence of the anchor situation in the world of evaluation, i.e., the rule has not been issued or has not been in place. There are no conclusions to be drawn about the situations where this rule is being followed. Either with or without negation, the situations in which this rule is being followed may or may not have taken place in the world of evaluation.

The anchor situation of deontic -al is a situation of a rule being in place. Since this is a stative situation description, it is expected that deontic -al behaves like a stative predicate. The question of why this has to be a generic state (or an individual-level predicate) remains for future research.

6.3.3. Causal Modality

There are four causal modals that are discussed in this paper: ‘let’ causative (existential), ‘make’ causative (universal), causal qoj (existential), and causal -al (existential). All causal modals except qoj trigger an actuality entailment, and all existential causal modals trigger an anti-actuality entailment under negation.

(120)	Causal modals in Balkar
	Modal	Flavor	Force	Aktionsart	Actuality Entailments	Anti-Actuality Entailments
	‘Make’ causative Agent	Causal	□	(Non-culminating) accomplishment	Yes	No
	‘Make’ causative Causer	Causal	⋄	Accomplishment	Yes	Yes
	‘Let’ causative Agent/Causer	Causal	⋄	Accomplishment	Yes	Yes
	-al (‘poss’)	Causal	⋄	Accomplishment	Yes	Yes
	qoj (‘allow’)	Causal	⋄	Accomplishment	No	Yes

The proposed theory of causal modality consists of two assumptions, repeated in (121).

(121)	Causal Modality Theory:
	a.	Modals with causal flavor quantify over causal chains initiated by the counterparts of the anchor situation.
	b.	Some existential modals with causal flavor introduce a conditional presupposition: if some counterpart of the anchor situation caused another situation, then the anchor situation caused the same situation.

The first assumption (121a) entails two things: (a) all and only existential causal modals trigger an anti-actuality entailment (‘let’ causatives, causal qoj (‘allow’), and causal -al), and (b) universal causal modals trigger an actuality entailment if not embedded under the imperfective or the delimitative operator (‘make’ causatives). The second assumption (121b) entails the existence of actuality entailments for certain existential causal modals (‘let’ causatives and causal -al).

Let us begin with the first assumption. Causal modals quantify over causal chains initiated by the counterparts of the anchor situation, which means that the causal accessibility relation is defined as follows:

(122)	For any pair of situations s and s${}^{\prime }$,
	Caus(s)(s${}^{\prime }$) if and only if ∃s${}^{″}$: C(s)(s${}^{″}$) and C-Chain(s${}^{″}$) = s${}^{\prime }$.

The meanings of the causal modal operators in Balkar are given below:

(123)	a.	$\left[\right[$caus□,caus${\left]\right]}^{w,g}$ = $\lambda$p. $\lambda$x. $\lambda$s: x⪯s and Causer(x)(s). ∀s${}^{\prime }$: Caus(s)(s${}^{\prime }$) → p(s${}^{\prime }$).
	b.	$\left[\right[$caus⋄,caus${\left]\right]}^{w,g}$ = $\lambda$p. $\lambda$x. $\lambda$s: x⪯s and Causer(x)(s). ∃s${}^{\prime }$: Caus(s)(s${}^{\prime }$) and p(s${}^{\prime }$).
	c.	$\left[\right[$ qoj⋄,caus${\left]\right]}^{w,g}$ = $\lambda$p. $\lambda$x. $\lambda$y. $\lambda$s: x⪯s, y⪯s and Causer(y)(s). ∃s${}^{\prime }$: Caus(s)(s${}^{\prime }$) and p(s${}^{\prime }$).
	d.	$\left[\right[$ al⋄,caus${\left]\right]}^{w,g}$ = $\lambda$p. $\lambda$x. $\lambda$s: x⪯s. ∃s${}^{\prime }$: Caus(s)(s${}^{\prime }$) and p(s${}^{\prime }$).

After the modals in (123) are fed their prejacent and their other arguments, the resulting meaning is a predicate over situations. In the case of the ‘make’ causative, this predicate looks as follows:

(124)	a.	[it-ni       awru-u     [Alim-ge  darman-la    al]vP-dɨr]CausP-ʁan-dɨ
		dog-gen fall.sick-3 Alim-dat medicine-pl take-caus-pst2-3
		‘The dog’s sickness made Alim buy medicine.’
	b.	$\left[\right[$ CausP ${\left]\right]}^{w,g}$ = $\lambda$s: the dog’s sickness ⪯ s and Causer(the dog’s sickness)(s).
		∀s${}^{\prime }$: Caus(s)(s${}^{\prime }$) → Alim buys medicine in s${}^{\prime }$.

The proposition in (124b) is true in a situation s if and only if s is a situation where the dog’s sickness is the Causer and, for every causal chain s′ initiated by a counterpart of s in some possible world, it is true that Alim buys medicine in s′.

The meaning of the CausP of a ‘let’ causative is given in (125).

(125)	a.	[it-ni        zuqla-ʁan-ɨ  [maŋa   tabaʁ-ɨ-n    al]vP-dɨr]CausP-ʁan-dɨ
		dog-gen sleep-nzr-3  1sg.dat plate-3-acc take-caus-pst2-3
		‘The dog’s sleeping let me take its plate.’
	b.	$\left[\right[$ CausP ${\left]\right]}^{w,g}$ = $\lambda$s: the dog’s sleeping ⪯ s and Causer(the dog’s sleeping)(s) .
		∃s${}^{\prime }$: Caus(s)(s${}^{\prime }$) and the speaker takes the dog’s plate in s${}^{\prime }$.

The proposition in (125b) is true in a situation s if and only if s is a situation where the dog’s sleeping is the Causer and there is a causal chain s′ initiated by a counterpart of s in some possible world in which the speaker takes the dog’s plate.

The meaning of ModP headed by causal qoj is given in (126).

(126)	a.	[it-ni        zuqla-ʁan-ɨ maŋa1    [pro1 tabaʁ-ɨ-n      al-ɨr-ʁa]TP      qoj]ModP-du
		dog-gen sleep-nzr-3 1sg.dat             plate-3-acc take-fut-dat allow-pst1
		‘The dog’s sleeping gave me an opportunity to take its plate.’
	b.	$\left[\right[$ ModP ${\left]\right]}^{w,g}$ = $\lambda$s: the dog’s sleeping ⪯ s, the speaker ⪯ s and Causer(the dog’s sleeping)(s). ∃s${}^{\prime }$: Caus(s)(s${}^{\prime }$) and the speaker takes the dog’s plate in s${}^{\prime }$.

The proposition in (126b) is true in a situation s if and only if s is a situation that involves the dog’s sleeping and the speaker, with the dog’s sleeping being the Causer, and there is a causal chain s′ initiated by a counterpart of s in some possible world in which the speaker takes the dog’s plate.

Finally, the meaning of ModP headed by causal -al is given in (127).:

(127)	a.	otou-da	zarɨq	bol-ʁan-ɨ	ücün	[men	[kitap	oqu]vP-jal]ModP-ʁan-ma
		room-loc	bright	be-nzr-3	because	1sg	book	read-poss-pst2-1sg
		‘Because it was bright in the room, I was able to read a book.’
	b.	$\left[\right[$ ModP ${\left]\right]}^{w,g}$ = $\lambda$s: the sp-r ⪯ s. ∃s${}^{\prime }$: Caus(s)(s${}^{\prime }$) and the sp-r reads a book in s${}^{\prime }$.

The proposition in (127b) is true in a situation s if and only if s is a situation that involves the speaker26 and there is a causal chain s′ initiated by a counterpart of s in some possible world in which the speaker reads a book.

This analysis derives an anti-actuality entailment with existential causal modals (‘let’ causative, qoj, and -al) and an actuality entailment with universal ones (‘make’ causative). The crucial assumption is that the counterpart relation is a reflexive relation (see Section 6.2.2), that is, every situation is a counterpart of itself.

Let us consider the universal causal modal in (124) first. Let us suppose that the modal in (124b) is embedded under the past perfective. In this case, a complete anchor situation takes place in the world of evaluation (see Section 6.3.1). In addition, according to the meaning in (124b), all of the counterparts of the anchor situation initiate a causal chain for which the prejacent is true (Alim buys medicine). Since the anchor situation is a counterpart of itself, it also initiates a causal chain for which the prejacent is true. Hence, an actuality entailment arises: Alim buys medicine in the world of evaluation.

Let us suppose that the modal in (124b) is embedded under the episodic past imperfective. In this case, a part of the anchor situation takes place in the world of evaluation (see Section 6.3.1). According to the meaning in (124b), all of the counterparts of the anchor situation initiate a causal chain for which the prejacent is true (Alim buys medicine). Although the anchor situation is a counterpart of itself, it does not necessarily take place in the world of evaluation because of the imperfective aspect. As a result, the causal chain initiated by it also does not necessarily take place. Hence, we predict no actuality entailment: Alim may or may not buy medicine in the world of evaluation.

Let us suppose now that the modal in (124b) is embedded under negation. In this case, we derive the following proposition: ¬∀s′: Caus(s)(s′) → Alim buys medicine in s′, where s is the anchor situation. That is, not all counterparts of the anchor situation initiate a causal chain where Alim buys medicine. From this, it also does not follow that the anchor situation initiates such a causal chain or that it does not. Hence, it also does not follow that Alim buys medicine in the world of evaluation or that he does not. No anti-actuality entailment is derived, as desired.

Now, let us consider the existential causal modals in (125), (126), and (127). Let us suppose that the modal in (125b) is embedded under negation. In this case, we derive the following proposition: ¬∃s′: Caus(s)(s′) and the speaker takes the dog’s plate in s′, where s is the anchor situation. That is, there is no counterpart of the anchor situation that initiates a causal chain where the speaker takes the dog’s plate. Since the anchor situation is a counterpart of itself, it follows that the anchor situation does not initiate a causal chain where the speaker takes the dog’s plate either. Hence, an anti-actuality entailment is derived: the speaker does not take the dog’s plate in the world of evaluation. The same is true for the existential modals in (126b) and (127b).

Let us suppose now that the modal in (125b) is embedded under the past perfective. In this case, a complete anchor situation takes place in the world of evaluation (see Section 6.3.1). According to the meaning in (125b), some counterpart of the anchor situation initiates a causal chain where the prejacent is true (the speaker takes the dog’s plate). It does not follow that the anchor situation itself initiates such a chain. No actuality entailment is derived. The same is true for the existential modals in (126b) and (127b). No actuality entailment is derived in the context of the episodic imperfective either.

In order to derive actuality entailments with existential causal modals, we need the additional assumption in (121b). Let us remember that not all existential causal modals have actuality entailments: ‘let’ causatives and causal -al do, but causal qoj does not. The assumption is that ‘let’ causatives and -al have an additional conditional presupposition.

(128)	a.	$\left[\right[$caus⋄,caus${\left]\right]}^{w,g}$ =
		$\lambda$p. $\lambda$x. $\lambda$s: x⪯s and Causer(x)(s) and $\boxed{({\exists s\mathrm{s}}^{\prime }:\mathrm{Caus(s)}({\mathrm{s}}^{\prime }\left)\mathrm{and}\mathrm{p}\right({\mathrm{s}}^{\prime })\to \mathrm{p}(\mathrm{C-Chain}\left(\mathrm{s}\right))}$. ∃s${}^{\prime }$:
		Caus(s)(s${}^{\prime }$) and p(s${}^{\prime }$).
	b.	$\left[\right[$ al⋄,caus${\left]\right]}^{w,g}$ =
		$\lambda$p. $\lambda$x. $\lambda$s: x⪯s and $\boxed{({\exists s\mathrm{s}}^{\prime }:\mathrm{Caus(s)}({\mathrm{s}}^{\prime }\left)\mathrm{and}\mathrm{p}\right({\mathrm{s}}^{\prime })\to \mathrm{p}(\mathrm{C-Chain}\left(\mathrm{s}\right))}$.
		∃s${}^{\prime }$: Caus(s)(s${}^{\prime }$) and p(s${}^{\prime }$).

The boxed presupposition in (128) guarantees that if some counterpart of the anchor situation caused a situation described by the prejacent, so did the anchor situation itself.

This straightforwardly derives an actuality entailment under the perfective. In this context, the anchor situation takes place in the world of evaluation and, as a result, brings about a situation described by the prejacent. Under the imperfective, only a part of the anchor situation takes place in the world of evaluation, so no actuality entailment is derived.

Under negation, no counterpart of the anchor situation initiates a causal chain where the prejacent is true. The conditional presupposition is trivially satisfied (its antecedent is false). The anchor situation, being a counterpart of itself, also does not initiate a causal chain where the prejacent is true. Thus, the explanation of anti-actuality entailments proposed above remains intact.

As for the lack of actuality entailments with the atelic interpretation of ‘make’ causatives with an Agent, this is derived with the application of the delimitative operator, which is crucially incompatible with all the other causal modals. Since the semantics of the delimitative operator is similar to that of the episodic imperfective in all the relevant respects (see Bar-el et al. 2005; Tatevosov 2008; Tatevosov and Ivanov 2009), its effect is predicted to be the same, namely, actuality entailments are canceled in the same way as culmination entailments are canceled with accomplishment predicates like open the door.

7. Conclusions

In this paper, I presented a study of deontic and causal modals in Balkar: two modal suffixes (the causative morpheme and -al) and two modal verbs (bujur (‘order’) and qoj (‘allow’)). This study provides preliminary evidence for the following three generalizations:

(129)	a.	Only causal modals can have actuality entailments (all universal ones and some existential ones).
	b.	Actuality entailments arise if and only if a causal modal is not embedded under an imperfective or a delimitative operator (whenever it has a telic interpretation).
	c.	Existential causal modals give rise to an anti-actuality entailment under negation.

In order to account for these generalizations, I propose a theory of deontic and causal modality within the framework of situation semantics. In this framework, root modals take a predicate over situations as their complement and return a predicate of situations.

Under the proposed theory, deontic modals quantify over situations that follow a particular rule or law and may or may not take place in the world of evaluation. This explains why deontic modals trigger neither actuality nor anti-actuality entailments. The proposed theory of causal modals consists of two key assumptions.

(130)	Causal Modality Theory:
	a.	Modals with causal flavor quantify over causal chains initiated by the counterparts of the anchor situation.
	b.	Some existential modals with causal flavor introduce a conditional presupposition: if some counterpart of the anchor situation caused another situation, then the anchor situation caused the same situation.

The first assumption (130a) makes two correct predictions: (a) all and only existential causal modals trigger anti-actuality entailments, and (b) universal causal modals trigger an actuality entailment. The reason is that the counterpart relation is a reflexive relation (every situation is a counterpart of itself). Thus, (130a) derives the generalization in (129c) and the part of the generalization in (129a) that concerns universal modals.

The second assumption (130b) predicts that certain existential causal modals (namely, the ones with the conditional presupposition) also trigger an actuality entailment. Thus, (130b) derives the part of the generalization in (129a) that concerns existential modals.

Causal Modality Theory treats modals with an actuality entailment as predicates of complex situations that consist of two sub-situations: the anchor situation and a situation described by the prejacent, with the latter being in the causal chain initiated by the former. This is the same meaning as that proposed for accomplishments by Dowty (1979), Levin and Rappaport-Hovav (1995), Paducheva (2004, 2009), Ramchand (2008), Tatevosov (2015), and others. As a result, modals that can have an actuality entailment only give rise to it in all cases in which the complete anchor situation takes place in the world of evaluation, in other words, only in all cases when they are not embedded under an imperfective or a delimitative operator. This accounts for the generalization in (129b).