关于无限哥德尔逻辑

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

Journal of Logic and Computation Pub Date : 2023-01-01 DOI:10.1093/logcom/exac040

Nicholas Pischke

引用次数: 0

摘要

我们研究了无限语言上的命题逻辑和一阶Gödel逻辑，这些逻辑在语义上是通过对单位区间$[0,1]$的相应解释来激发的。我们为具有可数长度的合/析的特定(命题和一阶)情形提供了无限hilbert式演算，并通过完全线性Heyting代数将通常的Lindenbaum-Tarski构造推广到相应代数语义的无限情形，证明了相应的完备性定理。给出了无限次超序微积分，并证明了相应的sch tte - tait型切消定理。对除$[0,1]$以外的真值集进行初始观察。

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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On infinitary Gödel logics

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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.