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Paraconsistent logic

About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.


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Journal ArticleDOI
01 Jan 2000-Synthese
TL;DR: Some conservative translations involving classical logic, Lukasiewicz three-valued system L3, the intuitionistic system I1 and several paraconsistent logics are presented.
Abstract: In 1999, da Silva, D'Ottaviano and Sette proposed a general definition for the term translation between logics and presented an initial segment of its theory. Logics are characterized, in the most general sense, as sets with consequence relations and translations between logics as consequence-relation preserving maps. In a previous paper the authors introduced the concept of conservative translation between logics and studied some general properties of the co-complete category constituted by logics and conservative translations between them. In this paper we present some conservative translations involving classical logic, Lukasiewicz three-valued system L 3, the intuitionistic system I 1 and several paraconsistent logics, as for instance Sette's system P 1, the D'Ottaviano and da Costa system J 3 and da Costa's systems C n, 1≤ n≤ω.

14 citations

Journal ArticleDOI
TL;DR: The machinery of Batens’ approach is used to extend the paraconsistent approach to dialogical logic as developed by Rahman and Carnielli to obtain a dynamic mechanism for the systematic study of dialogues in which two parties exchange arguments over a central claim, in the possible presence of inconsistencies.
Abstract: Even when inconsistencies are present in our premise set, we can sensibly distinguish between good and bad arguments relying on these premises. In making this distinction, the inconsistency-adaptive approach of Batens strikes a particularly nice balance between inconsistency-tolerance and inferential strength. In this paper, we use the machinery of Batens’ approach to extend the paraconsistent approach to dialogical logic as developed by Rahman and Carnielli. In bringing these frameworks closer together, we obtain a dynamic mechanism for the systematic study of dialogues in which two parties exchange arguments over a central claim, in the possible presence of inconsistencies.

14 citations

Book ChapterDOI
01 Jan 2009
TL;DR: A very plausible interpretation of what may be understood by a theory which encompasses complementarity in a definite sense is taken, which is term C-theories, which are non-trivial theories which may have ‘physically’ incompatible theorems.
Abstract: Bohr's Principle of Complementarity is controversial and there has been much dispute over its precise meaning. Here, without trying to provide a detailed exegesis of Bohr's ideas, we take a very plausible interpretation of what may be understood by a theory which encompasses complementarity in a definite sense, which we term C-theories. The underlying logic of such theories is a kind of logic which has been termed ‘paraclassical’, obtained from classical logic by a suitable modification of the notion of deduction. Roughly speaking, C-theories are non-trivial theories which may have ‘physically’ incompatible theorems (and, in particular, contradictory theorems). So, their underlying logic is a kind of paraconsistent logic.

14 citations

Proceedings ArticleDOI
26 Sep 2006
TL;DR: In this paper the author proposes non-Archimedean multiple-validity and construct the logical language with the related semantics and built non-ARCHIMedean valued sequent logic.
Abstract: In this paper I propose non-Archimedean multiple-validity and construct the logical language with the related semantics. Further I build non-Archimedean valued sequent logic. Notice that non-Archimedean valued logical system is considered for the first time. The Polish logician Jan Lukasiewicz began to create systems of many-valued logic, using a third value "possible" to deal with Aristotle?s paradox of the sea battle. Now many-valued logic has applications in diverse fields. In the earlier years of development of multiple-validity idea, the most promising field of its application is artificial intelligence. This application concerns vague notions and commonsense reasoning, e.g. in expert systems. In this context fuzzy logic is also interesting, because multiple-validity is modeled in artificial intelligence via fuzzy sets and fuzzy logic. There exist various many-valued logical systems. However non-Archimedean valued logic isn?t yet constructed. The idea of non-Archimedean multiple-validity is that (1) the set of truth values is uncountable infinite and (2) this set isn?t well-ordered. This idea can have a lot of applications in probabilistic reasoning (see [4, 1]).

14 citations

01 Jan 2002
TL;DR: It is shown that some paraconsistent logics and inconsistency-adaptive logics serve exactly the same purpose as some modallogics and ampliative adaptive logics based on S5, however, they serve this purpose along very different roads and the logics cannot be defined from one another.
Abstract: This paper concerns some connections between paraconsistent logics, modal logics (mainly S5), and Ambiguity Logic AL (Classical Logic applied to a language in which all letters are indexed and in which quantifiers over such indices are present). S5 may be defined from AL. Three kinds of connections will be illustrated. First, a paraconsistent logic A is presented that has the same expressive power as S5. Next, I consider the definition of paraconsistent logics from S5 and AL. Such definition is shown to work for some logics, for example Priest's LP. Other paraconsistent logics appear to withstand such definition, typically those that contain a detachable material implication. Finally, I show that some paraconsistent logics and inconsistency-adaptive logics serve exactly the same purpose as some modal logics and ampliative adaptive logics based on S5. However, they serve this purpose along very different roads and the logics cannot be defined from one another. The paper intends to open lines of research rather than pursuing them to the end. It also contains a poor person's semantics for S5 as well as a description of the simple but useful and powerful AL.

14 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202255
202131
202036
201935
201847