Analyticity with extra-logical information

IF 0.7 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Journal of Logic and Computation Pub Date : 2024-04-05 DOI:10.1093/logcom/exae013

Mario Piazza, Matteo Tesi

引用次数: 0

Abstract

In this paper, a new approach to the issue of extra-logical information within analytic (i.e. obeying the sub-formula property) sequent systems is introduced. We prove that incorporating extra-logical axioms into a purely logical system can preserve analyticity, provided these axioms belong to a suitable class of formulas that can be decomposed into a set of equivalent initial sequents and are permutable over the cut rule. Our approach is applicable not only to first-order classical and intuitionistic logics, but also to substructural logics. Furthermore, we establish a limit for the augmented systems under analysis: exceeding the boundaries of their respective classes of extra-logical axioms leads to either a loss of analyticity or a loss of structural properties.

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利用逻辑外信息进行分析

本文引入了一种新方法来解决解析（即遵守子公式属性）序列系统中的逻辑外信息问题。我们证明，在纯逻辑系统中加入逻辑外公理可以保持解析性，前提是这些公理属于一类合适的公式，可以分解成一组等价的初始序列，并且在切割规则上是可变的。我们的方法不仅适用于一阶经典逻辑和直觉逻辑，也适用于子结构逻辑。此外，我们还为所分析的增强系统建立了一个极限：超出各自逻辑外公理类的边界，要么会导致分析性的丧失，要么会导致结构特性的丧失。

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.