基于对等体的量化时间逻辑

IF 1.2 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Journal of Logical and Algebraic Methods in Programming Pub Date : 2025-08-13 DOI:10.1016/j.jlamp.2025.101082

Fabio Gadducci , Andrea Laretto , Davide Trotta

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引用次数: 0

摘要

这项工作的目的是从几个角度提出基于对应物的量化时间逻辑。我们首先介绍基于对应物范式的（一阶）线性时间逻辑的基于集合的语义，以及在部分函数和（可能重复的）关系的情况下其正范式的结果。然后，通过关系预捆引入了逻辑的范畴语义。通过正范式及其范畴语义的逻辑表示都使用证明助手Agda进行形式化，并且我们强调了我们的实现的关键方面以及在建设性证明助手中（量化）时间逻辑的实际使用。

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Counterpart-based Quantified Temporal Logics

The aim of this work is to present counterpart-based quantified temporal logics from several points of view. We start by introducing a set-based semantics for a (first-order) linear temporal logic based on the counterpart paradigm, along with results on its positive normal form both in the case of partial functions and of (possibly duplicating) relations. Then, a categorical semantics of the logic is introduced by means of relational presheaves. Both the presentations of the logic via the positive normal form and its categorical semantics are formalised using the proof assistant Agda, and we highlight the crucial aspects of our implementation and the practical use of (quantified) temporal logics in a constructive proof assistant.

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来源期刊

Journal of Logical and Algebraic Methods in Programming COMPUTER SCIENCE, THEORY & METHODS-LOGIC

CiteScore

2.60

自引率

22.20%

发文量

期刊介绍： The Journal of Logical and Algebraic Methods in Programming is an international journal whose aim is to publish high quality, original research papers, survey and review articles, tutorial expositions, and historical studies in the areas of logical and algebraic methods and techniques for guaranteeing correctness and performability of programs and in general of computing systems. All aspects will be covered, especially theory and foundations, implementation issues, and applications involving novel ideas.