Changing the logic without changing the subject: the case of computability

IF 0.7 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Journal of Logic and Computation Pub Date : 2024-04-02 DOI:10.1093/logcom/exae015

Francisco N MartÍnez-Aviña

引用次数: 0

Abstract

In this paper, I argue against the thesis that the meaning of ‘computability’ is logic-dependent. I do this from a category-theoretic perspective. Applying a method due to Mortensen and Lavers [26], I show that we can dualize the internal logic of the effective topos, in order to obtain a model of paraconsistent computability theory. Since the dualization leaves the structural properties of universal constructions in the topos unchanged, in particular the properties of the natural numbers object, I conclude that, at least in this case, changing the logic does not change our characterization of computability.

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改变逻辑而不改变主题：可计算性案例

在本文中，我将反驳 "可计算性 "的含义取决于逻辑的论点。我是从范畴论的角度来论证的。我运用莫滕森和拉维斯[26]的方法，证明我们可以把有效拓扑的内部逻辑二元化，从而得到一个准一致性可计算性理论的模型。由于二元化保持了拓扑中普遍构造的结构属性不变，特别是自然数对象的属性不变，我的结论是，至少在这种情况下，改变逻辑并不会改变我们对可计算性的描述。

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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