**2. The Trope Ontology**

Given the relative obscurity of the trope ontology, I will provide a brief overview here. For more detail, see my previous research [11].

The trope ontology is grounded in a view that relations between entities are real and exist primarily as individual relations, rather than universal relations. For example, when John stands next to Jane, it is not just John and Jane who exist, but also the relation of John's standing next to Jane. If John is also standing next to Jake, then that "standing next to" has a distinct existence from the "standing next to" of John and Jane. Moreover, these individual "standing next to" relations cannot exist without the entities that they bind. This strong dependence of relations on their relata supports calling such entity/relation constructions "tropes", although it represents only one view of tropes [12]. Philosophically, I have defended tropes by following Armstrong's reasoning [14] towards particularized universals, but rejecting Armstrong's argumen<sup>t</sup> that "states of a ffairs" are needed to bind relations to objects [11] (pp. 29–30). In this way, particularized relations (tropes) become an alternative theory that underpins relational realism. At the applied level, this results in individually identifiable relations, which provide a very convenient way to implement change and causal relations (discussed below).

Methodologically, I try to adhere to parsimony and minimize the di fferent kinds of relations that are admitted into the ontology, if for no other reason than the e ffort required to carefully examine

each relation for coherence in the ontology. On the other hand, one typically tries to choose relations that are as expressive as possible—i.e., relations with which one can say or represent as much as possible. So, the key principle of parsimonious expressiveness (or "say the most with the least") guides much of the work in the trope ontology. As such, the trope ontology is based on two main kinds of relations: mereological parthood and a primitive causality relation that ranges over the parthood relations. The semantics and formal properties of these relations are as follows.

The two primitive relations are represented with a simple predicate schema:

$$p(N, \text{part}, X, \mathcal{Y}),\tag{1}$$

$$p(M, \text{cause}, A, B),\tag{2}$$

Here, *N* and *M* represent unique identifiers for each relation, typically constructed as a list of numerals3. The second argumen<sup>t</sup> in the predicate is the kind of relation (e.g., part or cause) and the remaining arguments represent the entities that the relation binds.

A small digression is needed on the meaning of "kind of relation" in the context of trope theory. At first glance, it seems that "kind" introduces universals again. For instance, each individual parthood relation seems to instantiate a universal parthood. Might this not undermine the supposed "fundamental difference" (asserted in the introduction) between the trope ontology and a universal-based ontology like BFO? The short answer is "no", for the following reasons. Firstly, these are not the universals you are looking for. BFO distinguishes between universals (i.e., what members of certain classes of entities have in common) and relations such as "instantiates" or "has participant" [8] (p. 7). There is a sense in which universals in BFO are more complex entities (e.g., *cells*, *flasks* or *currency notes*) than the comparatively bare relations. Secondly, even if we admitted that relations have characteristics like universals, it does not oblige a trope ontologist to commit to relations *as universals*. There are two common realist options other than universals [12]. One is to posit resemblance as primitive, so that tropes are *resembling tropes* without having to distinguish "resemblance" from a relation like parthood. An alternative option is to posit a higher order resemblance relation, which avoids vicious regress by supervening on "lower level" particulars. The trope ontology is based on the former (i.e., *resembling tropes* as primitives) as it is the simpler of the two. In case "simplicity" seems like an inadequate justification, it should be noted that a choice of "primitives" needs to be accepted, at some level, in any ontology. Moreover, primitives are preferred where they reduce the number of ancillary ontological commitments needed (i.e., commitments that are needed only to maintain coherence, rather than to do the main "definitional" ontology work). Arguably, this is based on no more than a philosophical stance away from an "overpopulated universe [that] is in many ways unlovely" [15], but I shall nevertheless let it rest on that.

The specific kinds of relations and their arguments can be expanded for particular domain ontologies, but the core of the trope ontology has at least the parthood and causal relations. The parthood relation is formally defined through the axioms of General Extensional Mereology [16] (pp. 31–37). Note that I interpret general sums here as any collection of individuals under some meaningful relation, and not arbitrary collections [11] (p. 73), leaving the discussion of "meaningful" to individual cases.<sup>4</sup> Furthermore, it is important to understand parthood in a general sense in the trope ontology. For example, John's hand is part of him and therefore part of John's family, even though the hand is arguably part of John in a different way than John's being part of his family. However, the meaning of parthood is understood in the context of the relata of *hand* and *family*. This approach follows Eschenbach and Heydrich [17] by combining a general mereology with restricted domains.

<sup>3</sup> The use of lists of numerals as identifiers helps with the inference of transitive relations. For example, if we have p([1], part, a, b) and p([2], part, b, c), then we can infer p([1,2], part, a, c), where [1,2] represents the unique identifier for the a-c parthood relation.

<sup>4</sup> This stipulation supports a matching to the universals, discussed later.

The causal relation is transitive, irreflexive, anti-symmetric and ranges over parthood relations (and possibly other relations, if such relations exist within a specific domain ontology that is based on the trope ontology) [11] (pp. 86–96). The justification of causal primitives follows the reasoning of causal singularists like Richard Taylor [18], who argue that causality like "the fire started because of the lightning" has a stronger connection than mere constant conjunction (like "the fire started and there was lightning"). Moreover, singularists would also argue that the laws or rules that are often posited as underpinning causal relations merely describe the very causal relations that exist in the world [11] (pp. 86–90). In the trope ontology, we end up with a primitive causal relation that ranges over other relations—in particular over the individual parthood relations. The causal relation in the trope ontology should be understood as a "simple" relation that merely represents a linkage between an antecedent situation and its consequential situation in terms of the primitive relations (e.g., parthood) that the causal relation ranges over. This means that, in contemporary language, relations that are not ordinarily thought of as "causes" may indeed be causes in the ontology. For example, if John intentionally moves from Sydney to Melbourne, then both his intention and his prior being in Sydney are causal antecedents to his being in Melbourne. The way that John's being in Sydney is a causal antecedent to his being in Melbourne is similar to Aristotle's material cause, whereas John's intention is more aligned with a final cause [19] (94b.3).

The causal relations are *replacement* relations, in that the consequence replaces the antecedent. For example, if "John's being part of Sydney" causes "John's being part of Melbourne" then "John's being part of Sydney" no longer exists<sup>5</sup> at the end of that causal chain. This also applies in cases where arguably the antecedent could persist. For example, if "John's desire to be in Melbourne" causes him to be in Melbourne, it might be that his desire persists even when he is in Melbourne. Insofar as the causal relation reflects a change between situations, we must decide that either relations persist from the antecedent by default, or that they perish by default. The physical world indicates that antecedents are replaced by their consequent, therefore relations perish by default. For example, the relation of "John being in Sydney" perishes in the causal process. However, this implies that persistent antecedents must be explicitly renewed as additional consequences. Thus, if John's desire causes him to be in Melbourne and his desire persists, then, in order to persist, his antecedent desire must also cause (i.e., renew) his further desire. There is a certain level of representational choice in this part of the ontology, because one could assert persistence as the default representation (with explicit assertion of perishing relations). For example, in the case where John's walking and his intention to walk cause him to (keep) walking, one might argue that the physical situation persists by default. However, it seems that linguistically at least, we tend to interpret physical relations as perishing under causation, and this is what the trope ontology orients on.

The trope ontology is further extended with support for multiple worlds, represented with additional structure in the identifiers. For example, p([w:1], part, john, kitchen) might represent the relation that john is in the kitchen in world *w* (where *w* stands for some identifier). These multiple worlds form the basis for a modal description of the ontology, where we can talk of "possibility" and "necessity" [11] (pp. 108–114). In this case, I use the causal relation as the *accessibility relation* between worlds [20]. For instance, if John currently is in one room of a house, then it is possible that John can be in another room by asserting that John's being in one room (in the current world) is cause for John's being in another room (in another world). The stipulation of di fferent worlds enables us, in this case, to interpret "cause" modally as "may cause". Note that using the causal relation as the basis of accessibility means that the ontology can only support a modal logic that stops short of *normal modal logic* ("S5" in Kripke semantics [20]). Rather, the modal logic that is supported is S4 plus anti-symmetry.

Worlds also support the representation of informational states of entities. That is, the content of such an informational state—i.e., the *information*—can be represented with the same kinds of predicates

<sup>5</sup> "exists" in the sense of John's location in the physical world.

as used for the rest of the ontology, but isolated in their own world. For example, we might represent that John is thinking about being in Melbourne as,

p([0:1],part, thinking(1), 'John'). p([1:10], part, 'John', 'Melbourne').

The representation uses "reserved" functional terms such as thinking (1) to refer to an informational state, the *content* of which is represented by the predicates with the world indicator (1). Predicates with di fferent world indicators are isolated from each other. It is only the informational state (in this case, "thinking") as a whole that exists as part of John, not the relations within the informational state. This isolation is necessary to avoid that whatever John thinks also automatically exists in the world outside his thoughts. So, just because John *thinks* he is in Melbourne, does not mean he *is* in Melbourne—his thinking and the physical universe are two di fferent worlds. Assertion of informational states provides the pathway for defining core elements of the sociotechnical domain ontology that the trope ontology was first concerned with. That is, agentive "intentions" are defined as information states of some entity (i.e., the agent). Those information states (e.g., the state of neurons, or the magnetic state of electronic memory) may cause subsequent situations in the world.

The trope ontology is not only particularist in its view of relations, but also particularist in scope and intent. That is, trope ontologies will typically be limited to particular domains or investigations. The aim is not that such ontologies are complete in their own right but can be used as modules in a network of ontologies. Moreover, there is allowance for enhancements or even corrections of ontologies. As such, ontological inferences on a certain domain ontology that is based on the trope ontology will necessarily be limited to that domain ontology. To put it another way, inferences for a particular ontology do not necessarily hold when that ontology is changed, or when other ontologies are added. However, that limitation also enables us to make a simplifying<sup>6</sup> "closed world" assumption for inferences on the ontology. That is, any inferences are particular to a specific ontology and do not extend beyond unless explicit linking is asserted.

The trope ontology was intended as a foundation for constructive exploration of ontology, where one adds elements to the ontology based on particular cases. That is, in exploring the ontology of a domain, one starts by attempting to describe particular cases or examples of situations or states of affairs in that domain. Such attempts will highlight the kinds of entities and relations that an ontology needs to represent. The core of the trope ontology provides the sca ffolding of basic relations that is suggestive of how as ye<sup>t</sup> undefined terms or relations might work. For example, we might begin investigating an ontology of migration by trying to express John's intended move between cities. With parthood, causation and informational states we might attempt a simple version like, "John is part of Melbourne, because John was a part of Sydney; and John intended that John will be a part of Melbourne." So far, the example ontology is severely incomplete. That is, entities like John and the cities are captured as undi fferentiated entities in the ontology. Similarly, we are using a generic relation like parthood only to capture the general idea of what is happening in this case, but we would likely need more details to capture the semantics of "existing in a city". However, it is exactly these attempts at definition with a minimal ontology that reveal where more definition is needed, and thus supporting an iterative process of construction, inferential testing, and elaboration of the ontology.

At the practical level, the trope ontology is implemented as a logic program, with utilities to convert to other formats. In particular, programs are available to convert to and from "controlled natural language" statements [21]. Sentences like the one above (John's move) can be entered as plain text and are then converted to collections of predicates that comprise the ontology.

<sup>6</sup> Simplifying in the sense of making one closed world assumption for the ontology, rather than asserting for example the scope of each class. An overall closed world assumption also enables e fficient inference in certain logics, such as the logic programming language Prolog.
