Implicational Kleene algebra with domain and the substructural logic of partial correctness

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Mathematical Structures in Computer Science Pub Date : 2024-03-04 DOI:10.1017/s0960129524000045

Igor Sedlár

引用次数: 0

Abstract

We show that Kozen and Tiuryn’s substructural logic of partial correctness Abstract Image $\mathsf{S}$ embeds into the equational theory of Kleene algebra with domain, $\mathsf{KAD}$. We provide an implicational formulation of $\mathsf{KAD}$ which sets $\mathsf{S}$ in the context of implicational extensions of Kleene algebra.

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带域的隐含克莱因代数和部分正确性的子结构逻辑

我们证明 Kozen 和 Tiuryn 的部分正确性子结构逻辑 $\mathsf{S}$ 嵌入了有域 Kleene 代数的等式理论 $\mathsf{KAD}$ 中。我们提供了$\mathsf{KAD}$的蕴涵式表述，它将$\mathsf{S}$置于克莱因代数的蕴涵式扩展中。

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

Mathematical Structures in Computer Science 工程技术-计算机：理论方法

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.