Topic
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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TL;DR: This paper offers an alternative approach via a monotonic multiple-conclusion version of LP, the dual of Strong Kleene or K3, via an LP-based nonmonotonic logic due to Priest.
Abstract: Philosophical applications of familiar paracomplete and paraconsistent logics often rely on an idea of ‘default classicality’. With respect to the paraconsistent logic LP (the dual of Strong Kleene or K3), such ‘default classicality’ is standardly cashed out via an LP-based nonmonotonic logic due to Priest (1991, 2006a). In this paper, I offer an alternative approach via a monotonic multiple-conclusion version of LP.
63 citations
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01 Jan 1994
TL;DR: Vivid knowledge representation and reasoning with partiality, paraconsistency and constructivity and Lindenbaum-algebraic semantics of logic programs.
Abstract: General introduction.- Vivid knowledge representation and reasoning.- Partiality, paraconsistency and constructivity.- Vivid reasoning on the basis of facts.- Lindenbaum-algebraic semantics of logic programs.- Logic programming with strong negation and inexact predicates.- Vivid reasoning on the basis of rules.- Further topics, open problems.
63 citations
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TL;DR: It is shown that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal, and for every n > 2 there exists an extensive family of ideal n-valued logics.
Abstract: We define in precise terms the basic properties that an `ideal propositional paraconsistent logic' is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. Then we show that for every n > 2 there exists an extensive family of ideal n-valued logics, each one of which is not equivalent to any k-valued logic with k < n.
63 citations
01 Jan 2003
TL;DR: In this paper, the authors reexamine the foundations of linear logic and develop a system of natural deduction following Martin-L¨ of the separation of judgments from propositions, which accounts for multiplicative, additive, and exponential connectives.
Abstract: We reexamine the foundations of linear logic, developing a system of natural deduction following Martin-L¨ of’s separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva’s full intuitionistic linear logic. We also provide a corresponding sequent calculus that admits a simple proof of the admissibility of cut by a single structural induction. Finally, we show how to interpret classical linear logic (with or without the MIX rule) in our system, employing a form of double-negation translation.
62 citations
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01 Jan 2007
TL;DR: This chapter discusses paraconsistent logic, in which contradictions do not entail everything, the roots of paraconsistency lie deep in the history of logic, and its modern developments date to just before the middle of the 20th century.
Abstract: This chapter discusses paraconsistent logic, in which contradictions do not entail everything. However, the roots of paraconsistency lie deep in the history of logic, its modern developments date to just before the middle of the 20th century. Since then, the paraconsistent logic have been proposed and constructed for many and for different reasons. The most philosophically challenging of these reasons is dialetheism, the view that some contradictions are true. The chapter discusses the history of paraconsistency and the history of dialetheism. The chapter also discusses the modern developments of paraconsistency and dialetheism, those since about 1950. Some important issues that bear on paraconsistency, or on which paraconsistency bears the foundations of mathematics, the notion of negation, and rationality are discussed in the chapter.
62 citations