Definability of Boolean Functions in Kripke Semantics

IF 0.6 3区数学 Q2 LOGIC

Notre Dame Journal of Formal Logic Pub Date : 2023-08-01 DOI:10.1215/00294527-2023-0011

Naosuke Matsuda

引用次数: 0

Abstract

A set F of Boolean functions is said to be functionally complete if every Boolean function is definable by combining functions in F. Post clarified when a set of Boolean functions is functionally complete (with respect to classical semantics). In this paper, by extending Post’s theorem, we clarify when a set of Boolean functions is functionally complete with respect to Kripke semantics.

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Kripke语义中布尔函数的可定义性

如果每个布尔函数都可以通过组合F中的函数来定义，那么一个布尔函数集F就被称为功能完备的。Post澄清了什么时候一组布尔函数集是功能完备的(相对于经典语义)。在本文中，通过扩展Post定理，我们澄清了关于Kripke语义的一组布尔函数何时是函数完备的。

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

Notre Dame Journal of Formal Logic MATHEMATICS-LOGIC

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Notre Dame Journal of Formal Logic, founded in 1960, aims to publish high quality and original research papers in philosophical logic, mathematical logic, and related areas, including papers of compelling historical interest. The Journal is also willing to selectively publish expository articles on important current topics of interest as well as book reviews.