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Mathematics
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Algebraic Modal Logic and Proof Theory
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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: 31 July 2024 | Viewed by 2002

Special Issue Editor

Prof. Dr. Minghui Ma

E-Mail Website
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

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • modal algebra
  • modal logic
  • proof theory

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 451
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 - 02 Jan 2024
Viewed by 987
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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