Some completeness results in derivational modal logic

IF 0.7 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Journal of Logic and Computation Pub Date : 2023-08-08 DOI:10.1093/logcom/exad047

Quentin Gougeon

引用次数: 0

Abstract

Alongside the traditional Kripke semantics, modal logic also enjoys a topological interpretation, which is becoming increasingly influential. In this paper, we present various developments related to the topological derivational semantics, based on the Cantor derivative operator. We provide several characterizations of the validity of the axioms of bounded depth. We also elucidate the topological interpretation of the axioms of directedness and connectedness—which come in different forms, all of which we examine. We then prove results of soundness and completeness for all of these logics, using a range of old and new techniques.

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派生模态逻辑的一些完备性结果

除了传统的Kripke语义外，模态逻辑还具有拓扑解释，其影响力越来越大。在本文中，我们提出了基于Cantor导数算子的拓扑派生语义的各种发展。我们给出了有界深度公理有效性的几个刻画。我们还阐明了直接性和连通性公理的拓扑解释，它们以不同的形式出现，我们对所有这些都进行了研究。然后，我们使用一系列新旧技术证明了所有这些逻辑的完备性和完备性结果。

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 and Computation 工程技术-计算机：理论方法

CiteScore

1.90

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Logic has found application in virtually all aspects of Information Technology, from software engineering and hardware to programming and artificial intelligence. Indeed, logic, artificial intelligence and theoretical computing are influencing each other to the extent that a new interdisciplinary area of Logic and Computation is emerging. The Journal of Logic and Computation aims to promote the growth of logic and computing, including, among others, the following areas of interest: Logical Systems, such as classical and non-classical logic, constructive logic, categorical logic, modal logic, type theory, feasible maths.... Logical issues in logic programming, knowledge-based systems and automated reasoning; logical issues in knowledge representation, such as non-monotonic reasoning and systems of knowledge and belief; logics and semantics of programming; specification and verification of programs and systems; applications of logic in hardware and VLSI, natural language, concurrent computation, planning, and databases. The bulk of the content is technical scientific papers, although letters, reviews, and discussions, as well as relevant conference reviews, are included.