Algebraic Completeness of Connexive and Bi-Intuitionistic Multilattice Logics

IF 0.7 3区数学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal of Logic Language and Information Pub Date : 2024-05-03 DOI:10.1007/s10849-024-09415-7

Yaroslav Petrukhin

引用次数: 0

Abstract

In this paper, we introduce the notions of connexive and bi-intuitionistic multilattices and develop on their base the algebraic semantics for Kamide, Shramko, and Wansing’s connexive and bi-intuitionistic multilattice logics which were previously known in the form of sequent calculi and Kripke semantics. We prove that these logics are sound and complete with respect to the presented algebraic structures.

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连立逻辑和双推理多网格逻辑的代数完备性

在本文中，我们引入了连生多格法和双直觉多格法的概念，并在其基础上发展了 Kamide、Shramko 和 Wansing 的连生多格法和双直觉多格法逻辑的代数语义，这些逻辑以前是以序列计算和克里普克语义的形式为人所知的。我们证明这些逻辑在所提出的代数结构方面是健全和完整的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Logic Language and Information COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCEL-LOGIC

CiteScore

1.70

自引率

12.50%

发文量

期刊介绍： The scope of the journal is the logical and computational foundations of natural, formal, and programming languages, as well as the different forms of human and mechanized inference. It covers the logical, linguistic, and information-theoretic parts of the cognitive sciences. Examples of main subareas are Intentional Logics including Dynamic Logic; Nonmonotonic Logic and Belief Revision; Constructive Logics; Complexity Issues in Logic and Linguistics; Theoretical Problems of Logic Programming and Resolution; Categorial Grammar and Type Theory; Generalized Quantification; Information-Oriented Theories of Semantic Structure like Situation Semantics, Discourse Representation Theory, and Dynamic Semantics; Connectionist Models of Logical and Linguistic Structures. The emphasis is on the theoretical aspects of these areas.