Four-Valued Logics of Truth, Nonfalsity, Exact Truth, and Material Equivalence

IF 0.6 3区 数学 Q2 LOGIC
Adam Přenosil
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引用次数: 1

Abstract

The four-valued semantics of Belnap–Dunn logic, consisting of the truth values True, False, Neither, and Both, gives rise to several nonclassical logics depending on which feature of propositions we wish to preserve: truth, nonfalsity, or exact truth (truth and nonfalsity). Interpreting equality of truth values in this semantics as material equivalence of propositions, we can moreover see the equational consequence relation of this four-element algebra as a logic of material equivalence. In this paper, we axiomatize all combinations of these four-valued logics, for example, the logic of truth and exact truth or the logic of truth and material equivalence. These combined systems are consequence relations which allow us to express implications involving more than one of these features of propositions.
真、非真、精确真和物质等价的四值逻辑
Belnap-Dunn逻辑的四值语义由真值True、False、Noter和Both组成,根据我们希望保留命题的哪个特征,产生了几个非经典逻辑:真值、非伪值或精确真值(真值和非伪值)。将该语义中的真值相等解释为命题的物质等价,我们还可以将该四元代数的等价结果关系视为物质等价的逻辑。在本文中,我们公理化了这四值逻辑的所有组合,例如,真理与精确真理的逻辑或真理与物质等价的逻辑。这些组合系统是结果关系,使我们能够表达涉及命题的不止一个特征的含义。
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来源期刊
CiteScore
1.00
自引率
14.30%
发文量
14
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.
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