具有两个指定值的Kleene强三值矩阵自然隐含展开式的Belnap-Dunn语义

Q1 Arts and Humanities

Journal of Applied Non-Classical Logics Pub Date : 2019-01-02 DOI:10.1080/11663081.2018.1534487

G. Robles, J. Méndez

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引用次数: 17

摘要

条件句是自然的，如果它满足以下三个条件。(1)在限定于经典值T和F时，与经典条件重合;(2)满足本理依据;(3)每当赋给它的先行项的值小于或等于赋给它的后项的值时，它就被赋一个指定的值。本文的目的是为Kleene强3值矩阵具有两个指定元素的所有自然隐含展开式提供一个“二价”Belnap-Dunn语义。(我们根据N. Tomova，“正则Kleene逻辑的隐含扩展的晶格”来理解“自然条件”的概念，《数理逻辑报告》，47,173-182,2012。)

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Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values

ABSTRACT A conditional is natural if it fulfils the three following conditions. (1) It coincides with the classical conditional when restricted to the classical values T and F; (2) it satisfies the Modus Ponens; and (3) it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two designated elements. (We understand the notion ‘natural conditional’ according to N. Tomova, ‘A lattice of implicative extensions of regular Kleene's logics’, Reports on Mathematical Logic, 47, 173–182, 2012.)

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来源期刊

Journal of Applied Non-Classical Logics Arts and Humanities-Philosophy

CiteScore

1.30

自引率

0.00%

发文量