具有Gödel-type和对偶Gödel-type否定的Kleene强3值逻辑变体的自然隐含展开

Q1 Arts and Humanities

Journal of Applied Non-Classical Logics Pub Date : 2021-04-03 DOI:10.1080/11663081.2021.1948285

G. Robles, J. Méndez

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引用次数: 1

摘要

设MK3和MK3为Kleene强3值矩阵，分别只有一个和两个指定值。接下来，让MK3 (resp.)， MK3)被精确地定义为MK3(参见。， MK3)，只是Kleene强3值矩阵的特征Łukasiewicz-type否定被“Gödel-type”否定所取代(见1)。(' dual Gödel-type '否定)。本文的目的是公理化由MK3和MK3的所有自然隐含展开式所决定的逻辑。公理化公式是用“二值”Belnap-Dunn语义定义的。

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Natural implicative expansions of variants of Kleene's strong 3-valued logic with Gödel-type and dual Gödel-type negation

Let MK3 and MK3 be Kleene's strong 3-valued matrix with only one and two designated values, respectively. Next, let MK3 (resp., MK3 ) be defined exactly as MK3 (resp., MK3 ), except that the characteristic Łukasiewicz-type negation of Kleene's strong 3-valued matrix is replaced by a ‘Gödel-type’ negation (resp., ‘dual Gödel-type’ negation). The aim of this paper is to axiomatize the logics determined by all natural implicative expansions of MK3 and MK3 . The axiomatic formulations are defined by using a ‘two-valued’ Belnap-Dunn semantics.

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来源期刊

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

CiteScore

1.30

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0.00%

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