Paraconsistent logic

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

Theoretical Significance and Practical Value of Paraconsistent Logic

Abstract: Paraconsistent logic is the most revolutionary spirit in non-classical logic, it restricts the action of Non-Contradiction, and it can tolerate the true contradiction. Paraconsistent logic is the underlying logic of all paraconsistent theories, it has a wide useful foreground on aspects of computer, artificial intelligence and law etc.

The Relevance of Quantum Logic in the Domain of Non-Classical Logics

Abstract: Publisher Summary Quantum logic (QL) is a weak logic. Two kinds of semantical approaches have turned out to be particularly successful in the attempt to characterize the elements of the subuniverse of weak logics: the “algebraic” and the “Kripke-semantics.” Kripkian characterization of QL is referred in the chapter. The chapter defines the two notions of “epistemic” and “similarity-(Kripkian) realization” for a sentential language. The logic characterized by the class of all orthomodular similarity realizations has been called “orthomodular quantum logic” (OQL); and this logic has found successful applications to the logical analysis of quantum mechanics. An interesting feature of OQL is represented by the fact that in this logic one can define a well-behaved conditional connective in terms of negation and conjunction. Quantum logics give rise to some characteristic “metalogical anomalies” that lead to conjecture that the distinction between epistemic and similarity-logics represents a highly significant dividing line within the universe of weak logics. The chapter concludes that similarity-logics seem to bring about deep changes concerning some very basic and ancient questions of the foundations of logic.

Partial and paraconsistent approaches to future contingents in tense logic

Abstract: The problem of future contingents is regarded as an important philosophical problem in connection with determinism and it should be treated by tense logic. Prior’s early work focused on the problem, and later Prior studied branching-time tense logic which was invented (i.e. first suggested) by Kripke. However, Prior’s idea to use three-valued logic for the problem seems to be still alive. In this paper, we consider partial and paraconsistent approaches to the problem of future contingents. These approaches theoretically meet Aristotle’s interpretation of future contingents.

Toward a phenomenological epistemology of mathematical logic

Abstract: This paper deals with Husserl’s idea of pure logic as it is coined in the Logical Investigations (1900/1901). First, it exposes the formation of pure logic around a conception of completeness (Sect. 2); then, it presents intentionality as the keystone of such a structuring (Sect. 3); and finally, it provides a systematic reconstruction of pure logic from the semiotic standpoint of intentionality (Sect. 4). In this way, it establishes Husserlian pure logic as a phenomenological epistemology of mathematical logic.

A tableau algorithm for paraconsistent and nonmonotonic reasoning in description logic-based system

Abstract: This paper proposes a paraconsistent and nonmonotonic extension of description logic by planting a nonmonotonic mechanism called minimal inconsistency in paradoxical description logics, which is a paraconsistent version of description logics. A precedence relation between two paradoxical models of knowledge bases is firstly introduced to obtain minimally paradoxical models by filtering those models which contain more inconsistencies than others. A new entailment relationship between a KB and an axiom characterized by minimal paradoxical models is applied to characterize the semantics of a paraconsistent and nonmonotonic description logic. An important advantage of our adaptation is simultaneously overtaking proverbial shortcomings of existing two kinds extensions of description logics: the weak inference power of paraconsistent description logics and the incapacity of nonmonotonic description logics in handling inconsistencies. Moreover, our paraconsistent and nonmonotonic extension not only preserves the syntax of description logic but also maintains the decidability of basic reasoning problems in description logics. Finally, we develop a sound and complete tableau algorithm for instance checking with the minimally paradoxical semantics.