Dual counterpart intuitionistic logic

IF 0.7 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Journal of Logic and Computation Pub Date : 2023-09-11 DOI:10.1093/logcom/exad019

Anthony Cantor, Aaron Stump

引用次数: 0

Abstract

Abstract We introduce dual counterpart intuitionistic logic (or DCInt): a constructive logic that is a conservative extension of intuitionistic logic, a sublogic of bi-intuitionistic logic, has the logical duality property of classical logic, and also retains the modal character of its interpretation of the connective dual to intuitionistic implication. We define its Kripke semantics along with the corresponding notion of a bisimulation, and then prove that it has both the disjunction property and (its dual) the constructible falsity property. Also, for any class $ {\mathcal{C}}$ of Kripke frames from our semantics, we identify a condition such that $ {\mathcal{C}}$ will have the disjunction property if it satisfies the condition. This provides a method for generating extensions of DCInt that retain the disjunction property.

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对偶直觉逻辑

摘要:本文介绍了对偶对偶直觉逻辑(dual counterpart intuitionistic logic，简称DCInt):它是直觉逻辑的保守扩展，是双直觉逻辑的一个子逻辑，具有经典逻辑的逻辑对偶性质，同时又保留了其对直觉蕴涵的连接对偶解释的模态特征。我们定义了它的Kripke语义以及相应的双模拟概念，并证明了它具有析取性质和(它的对偶)可构造假性。同样，对于我们语义中的Kripke框架的任何类$ {\mathcal{C}}$，我们确定一个条件，使得$ {\mathcal{C}}$满足该条件就具有析取属性。这提供了一种方法来生成保留析取属性的DCInt扩展。

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.

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