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 1996
5 citations
01 Jan 2015
TL;DR: In this article, the authors describe how complement toposes, with their paraconsistent internal logic, lead to a more abstract theory of topos logic, including Beziau's ideas on logical structures, axiomatic emptiness and on logical many-valuedness.
Abstract: In this chapter, I describe how complement toposes, with their paraconsistent internal logic, lead to a more abstract theory of topos logic. Beziau’s work in Universal Logic – including his ideas on logical structures, axiomatic emptiness and on logical many-valuedness – is central in this shift and therefore it is with great pleasure that I wrote this chapter for the present commemorative volume.
5 citations
Journal Article•
TL;DR: This work proposes a constructive discursive logic with strong negation CDLSN based on Nelson’s constructive logic N and gives an axiomatic system and Kripke semantics with a completeness proof.
Abstract: Jaskowski’s discursive logic (or discussive logic) is the first formal paraconsistent logic which is classified as a non-adjunctive system It is now recognized that discursive logic is not generally appropriate for paraconsistent reasoning To improve it in a constructive setting, we propose a constructive discursive logic with strong negation CDLSN based on Nelson’s constructive logic N In CDLSN , discursive negation is defined similar to intuitionistic negation and discursive implication is defined as material implication using discursive negation We give an axiomatic system and Kripke semantics with a completeness proof We also discuss some advantages of the proposed system over other paraconsistent systems
5 citations
01 Jan 2006
TL;DR: In this paper, a natural deduction formulation for full intuitionistic linear logic (FILL) is described, which is a variant of multiplicative linear logic with intrinsic multiple conclusions, inspired by Parigot's natural deduction system for classical logic.
Abstract: This paper describes a natural deduction formulation for Full Intuitionistic Linear Logic (FILL), an intriguing variation of multiplicative linear logic, due to Hyland and de Paiva. The system FILL resembles intuitionistic logic, in that all its connectives are independent, but resembles classical logic in that its sequent-calculus formulation has intrinsic multiple conclusions. From the intrinsic multiple conclusions comes the inspiration to modify Parigot's natural deduction systems for classical logic, to produce a natural deduction formulation and a term assignment system for FILL.
5 citations