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: It is proved that a Paraconsistent Non-dependence Logic formula is consistent if and only if it is equivalent to some First Order Logic sentence; and it is shown that, on the other hand, all Paraconsistant Dependence Logic sentences are equivalent toSome First Order sentence with respect to truth (but not necessarily withrespect to falsity).
Abstract: We introduce a variant of Dependence Logic in which truth is defined not in terms of existence of winning strategies for the Proponent (Eloise) in a semantic game, but in terms of lack of winning strategies for the Opponent (Abelard). We show that this language is a conservative but paraconsistent extension of First Order Logic, that its validity problem can be reduced to that of First Order Logic, that it capable of expressing its own truth and validity predicates, and that it is expressively equivalent to Universal Second Order Logic. Furthermore, we prove that a Paraconsistent Non-dependence Logic formula is consistent if and only if it is equivalent to some First Order Logic sentence; and we show that, on the other hand, all Paraconsistent Dependence Logic sentences are equivalent to some First Order sentence with respect to truth (but not necessarily with respect to falsity).
2 citations
01 Jan 2007
2 citations
30 Mar 2018
2 citations
TL;DR: A non-adjunctive logic developed by P.K. Schotch and RE. Jennings as mentioned in this paper allows a tolerant attitude toward inconsistency while giving an account of reductive reasoning.
Abstract: Nicholas Rescher has argued we must tolerate inconsistency because of our cognitive limitations. He has also produced, together with R. Brandom, a serious attempt at exploring the logic of inconsistency. Inconsistency tolerance calls for a systematic rewriting of our logical doctrines: it requires a paraconsistent logic. However, having given up all aggregation of premises, Rescher's proposal for a paraconsistenl logic fails to account for the reductive reasoning Rescher appeals to in his account of inconsistency tolerance. A non-adjunctive logic developed by P.K. Schotch and RE. Jennings provides just what Rescher's logic is lacking: It allows a tolerant
attitude toward inconsistency while giving an account of reductive reasoning.
2 citations
23 May 1995
TL;DR: This paper describes paraconsistent circumscription by application of predicate circumscription in aParaconsistent logic, and in addition to circumscribe the predicates, the inconsistency is circumscribe.
Abstract: In this paper we describe paraconsistent circumscription by application of predicate circumscription in a paraconsistent logic. In addition to circumscribe the predicates, we also circumscribe the inconsistency. Paraconsistent circumscription can be well characterized by the minimal semantics that is both nonmonotonic and paraconsistent. It brings us advantages at least in two respects: nonmonotonic logic would be nontrivial while there was a contradiction, and paraconsistent logic would be equivalent to classical logic while there was no direct effect of a contradiction.
2 citations