Natural three-valued logics and classical logic
نویسندگان
چکیده
منابع مشابه
Three-valued Logics in Modal Logic
Every truth-functional three-valued propositional logic can be conservatively translated into the modal logic S5. We prove this claim constructively in two steps. First, we define a Translation Manual that converts any propositional formula of any threevalued logic into a modal formula. Second, we show that for every S5-model there is an equivalent three-valued valuation and vice versa. In gene...
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There are several three-valued logical systems. They give the impression of a scattered landscape. The majority of the works on this subject gives the truth tables, sometimes an Hilbert style axiomatization in a basic propositional language and a completeness theorem with respect to those truth tables. We show that all the reasonable connectives in three-valued logics can be built starting from...
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Several interpretations can be given to the third truth value in three-valued logics. Here, we consider the case when it refers to the epistemic notion of contradictory, or both true and false at the same time. We study several paraconsistent threevalued logics that carry this concern and show that they can be translated into a fragment of a simple epistemic logic where modalities can only appe...
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Every truth-functional three-valued propositional logic can be conservatively translated into the modal logic S5. We prove this claim constructively in two steps. First, we define a Translation Manual that converts any propositional formula of any threevalued logic into a modal formula. Second, we show that for every S5-model there is an equivalent three-valued valuation and vice versa. In gene...
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We consider propositional logic. Three-valued logics are old: the first one is Lukasiewicz three valued logic from 1920 [8]. Gödel in [5] from 1932 studied a hierarchy of finite-valued logics, containing Gödel three-valued logic. Our main interest pays to Kleene three-valued logic [6]. Other threevalued logics will not be considered here. Let us agree that the three truth values are 0, 1 2 , 1 ...
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ژورنال
عنوان ژورنال: Logical Investigations
سال: 2013
ISSN: 2413-2713,2074-1472
DOI: 10.21146/2074-1472-2013-19-0-344-352