Modal algebra of multirelations

IF 0.7 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Journal of Logic and Computation Pub Date : 2024-05-29 DOI:10.1093/logcom/exae023

Hitoshi Furusawa, Walter Guttmann, Georg Struth

引用次数: 0

Abstract

We formalize the modal operators from the concurrent dynamic logics of Peleg, Nerode and Wijesekera in a multirelational algebraic language based on relation algebras and power allegories, using relational approximation operators on multirelations developed in a companion article. We relate Nerode and Wijesekera’s box operator with a relational approximation operator for multirelations and two related operators that approximate multirelations by different kinds of deterministic multirelations. We provide an algebraic soundness proof of Goldblatt’s axioms for concurrent dynamic logic and one for a multirelational Hoare logic based on Nerode and Wijesekera’s box as applications.

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多重关系的模态代数

我们将佩雷格、内罗德和维杰塞克拉的并发动态逻辑中的模态算子用一种基于关系代数和幂寓言的多关系代数语言形式化，并使用了在另一篇文章中开发的多关系近似算子。我们将 Nerode 和 Wijesekera 的盒算子与多关系的关系近似算子和两个相关算子联系起来，这两个算子通过不同种类的确定性多关系近似多关系。我们提供了并发动态逻辑 Goldblatt 公理的代数合理性证明，以及基于 Nerode 和 Wijesekera 的盒算子的多关系 Hoare 逻辑的代数合理性证明。

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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