Algebraic Modal Logic and Proof Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 30 June 2025 | Viewed by 2946

Special Issue Editor


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Guest Editor
Institute of Logic and Cognition, Department of Philosophy, Sun Yat-Sen University, Guangzhou, China
Interests: Modal logic; non-classical logic; proof theory; model theory

Special Issue Information

Dear Colleagues,

Algebraic modal logic focuses on the study of modalities using the toolkit from universal algebra. In recent years, studies on non-classical modal logics from algebraic perspective have grown rapidly. Many results on Kripke completeness, duality, correspondence and lattice theoretic properties for these logics are established. Furthermore, algebraic proof theory of modal logics goes along diverse directions. Authors are encouraged to submit manuscripts closely related with these topics to this Special Issue.

Prof. Dr. Minghui Ma
Guest Editor

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Keywords

  • modal algebra
  • modal logic
  • proof theory

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Published Papers (2 papers)

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Research

13 pages, 291 KiB  
Article
Paraconsistent Labeling Semantics for Abstract Argumentation
by Yuanlei Lin
Mathematics 2024, 12(5), 688; https://doi.org/10.3390/math12050688 - 27 Feb 2024
Viewed by 750
Abstract
Dung’s abstract argumentation framework is a popular formalism in formal argumentation. The present work develops paraconsistent labeling semantics for abstract argumentation such that the incomplete and inconsistent information can be expressed, and it introduces a Hilbert-style axiomatic system which is proven to be [...] Read more.
Dung’s abstract argumentation framework is a popular formalism in formal argumentation. The present work develops paraconsistent labeling semantics for abstract argumentation such that the incomplete and inconsistent information can be expressed, and it introduces a Hilbert-style axiomatic system which is proven to be sound and complete. Additionally, we make a comparison between the logic developed in the present work and some relevant theories of abstract argumentation. Full article
(This article belongs to the Special Issue Algebraic Modal Logic and Proof Theory)
25 pages, 439 KiB  
Article
Merging Intuitionistic and De Morgan Logics
by Minghui Ma and Juntong Guo
Mathematics 2024, 12(1), 146; https://doi.org/10.3390/math12010146 - 2 Jan 2024
Viewed by 1363
Abstract
We introduce De Morgan Heyting logic for Heyting algebras with De Morgan negation (DH-algebras). The variety DH of all DH-algebras is congruence distributive. The lattice of all subvarieties of DH is distributive. We show the discrete dualities between De Morgan frames and DH-algebras. [...] Read more.
We introduce De Morgan Heyting logic for Heyting algebras with De Morgan negation (DH-algebras). The variety DH of all DH-algebras is congruence distributive. The lattice of all subvarieties of DH is distributive. We show the discrete dualities between De Morgan frames and DH-algebras. The Kripke completeness and finite approximability of some DH-logics are proven. Some conservativity of DH expansion of a Kripke complete superintuitionistic logic is shown by the construction of frame expansion. Finally, a cut-free terminating Gentzen sequent calculus for the DH-logic of De Morgan Boolean algebras is developed. Full article
(This article belongs to the Special Issue Algebraic Modal Logic and Proof Theory)
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