Valuation Semantics for S4

IF 0.6 3区数学 Q2 LOGIC

Studia Logica Pub Date : 2024-05-03 DOI:10.1007/s11225-024-10100-w

Andréa M. Loparić, Cezar A. Mortari

引用次数: 0

Abstract

This expository paper presents an application, to the modal logic S4, of the valuation semantics technique proposed by Loparić for the basic normal modal logic K. In previous works we presented a valuation semantics for the minimal temporal logic Kt and several other systems modal and temporal logic. How to deal with S4, however, was left as an open problem—although we arrived at a working definition of \(A_1,\ldots ,A_n\)-valuations, we were not able to prove an important lemma for correctness. In this paper we solve this, presenting valuations for S4.

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S4 的估值语义

这篇说明性论文介绍了洛帕里奇（Loparić）为基本正常模态逻辑K提出的估值语义学技术在模态逻辑S4中的应用。在以前的工作中，我们提出了最小时态逻辑Kt和其他几个系统模态逻辑和时态逻辑的估值语义学。然而，如何处理 S4 却成了一个悬而未决的问题--虽然我们得出了 \(A_1,\ldots ,A_n\)-估值的工作定义，但却无法证明一个重要的正确性lemma。在本文中，我们解决了这个问题，提出了 S4 的估值。

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

Studia Logica MATHEMATICS-LOGIC

CiteScore

1.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The leading idea of Lvov-Warsaw School of Logic, Philosophy and Mathematics was to investigate philosophical problems by means of rigorous methods of mathematics. Evidence of the great success the School experienced is the fact that it has become generally recognized as Polish Style Logic. Today Polish Style Logic is no longer exclusively a Polish speciality. It is represented by numerous logicians, mathematicians and philosophers from research centers all over the world.