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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01 Jan 1991
TL;DR: Cut-elimination is a central tool in proof-theory, but also a way of computing with proofs used for constructing new functional languages that depends on the properties of the deduction system in which proofs are written.
Abstract: Cut-elimination is a central tool in proof-theory, but also a way of computing with proofs used for constructing new functional languages. As such it depends on the properties of the deduction system in which proofs are written.
62 citations
60 citations
20 Jul 2009
TL;DR: The purpose of this essay is to shed some light on a certain type of sentence, which is a borderline contradiction, a sentence of the form Fa ∧¬Fa for some vague predicate F and some borderline case a of F, or a sentence equivalent to such a sentence.
Abstract: The purpose of this essay is to shed some light on a certain type of sentence, which I call a borderline contradiction. A borderline contradiction is a sentence of the form Fa ∧¬Fa, for some vague predicate F and some borderline case a of F, or a sentence equivalent to such a sentence. For example, if Jackie is a borderline case of ‘rich’, then ‘Jackie is rich and Jackie isn’t rich’ is a borderline contradiction. Many theories of vague language have entailments about borderline contradictions; correctly describing the behavior of borderline contradictions is one of the many tasks facing anyone offering a theory of vague language.
60 citations
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TL;DR: This paper shows that this ac- count gives a sound and complete semantics for Priest's paraconsistent logic LP, which uses materials any modal logician has at hand.
Abstract: Paraconsistent logics are often semantically motivated by consider- ing "impossible worlds." Lewis, in "Logic for equivocators," has shown how we can understand paraconsistent logics by attributing equivocation of mean- ings to inconsistent believers. In this paper I show that we can understand para- consistent logics without attributing such equivocation. Impossible worlds are simply sets of possible worlds, and inconsistent believers (inconsistently) be- lieve that things are like each of the worlds in the set. I show that this ac- count gives a sound and complete semantics for Priest's paraconsistent logic LP, which uses materials any modal logician has at hand.
60 citations
Book•
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TL;DR: The study of pure inductive logic as mentioned in this paper is the study of rational probability treated as a branch of mathematical logic, and it is the first approach devoted to this approach, bringing together the key results from the past seventy years plus the main contributions of the authors and their collaborators over the last decade to present a comprehensive account of the discipline within a unified context.
Abstract: Pure inductive logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years plus the main contributions of the authors and their collaborators over the last decade to present a comprehensive account of the discipline within a single unified context. The exposition is structured around the traditional bases of rationality, such as avoiding Dutch Books, respecting symmetry and ignoring irrelevant information. The authors uncover further rationality concepts, both in the unary and in the newly emerging polyadic languages, such as conformity, spectrum exchangeability, similarity and language invariance. For logicians with a mathematical grounding, this book provides a complete self-contained course on the subject, taking the reader from the basics up to the most recent developments. It is also a useful reference for a wider audience from philosophy and computer science.
60 citations