Paraconsistent logic

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

Paraconsistent Modal Logic

Abstract: Generalize the methods of paraconsistent fuzzy reasoning into modal logic, propose a paraconsistent modal logic, whose logical consequence is a modal extension of a paraconsistent fuzzy implication, which has the abilities of both handling inconsistency and representing multi world modals, and present its sound and complete Gentzen style inference system.

Paraconsistent Logic Programs with Four-Valued Rough Sets

Abstract: This paper presents a language for defining four-valued rough sets and to reason about them Our framework brings together two major fields: rough sets and paraconsistent logic programming On the one hand it provides a paraconsistent approach, based on four-valued rough sets, for integrating knowledge from different sources and reasoning in the presence of inconsistencies On the other hand, it also caters for a specific type of uncertainty that originates from the fact that an agent may perceive different objects of the universe as being indiscernible This paper extends the ideas presented in [9] Our language allows the user to define similarity relations and use the approximations induced by them in the definition of other four-valued sets A positive aspect is that it allows users to tune the level of uncertainty or the source of uncertainty that best suits applications

Combinators for Paraconsistent Attitudes

Abstract: In order to analyse the semantics of natural language sentences a translation into a partial type logic using lexical and logical combinators is presented. The sentences cover a fragment of English with propositional attitudes like knowledge, belief and assertion. A combinator is a closed term of the lambda calculus possibly containing lexical and/or logical constants. Such combinators seem promising from both a cognitive and computational point of view. There is approximately one lexical combinator for each word, but just eleven logical combinators for the present fragment. The partiality is only used for embedded sentences expressing propositional attitudes, thereby allowing for inconsistency without explosion (also called paraconsistency), and is based on a few key equalities for the connectives giving four truth values (truth, falsehood, and undefinedness with negative and positive polarity; only the first truth value is designated, i.e. yields the logical truths).

Sweet Reason: A Field Guide to Modern Logic

Abstract: Preface for the General Reader.- Preface for Logic Teachers: How to Use this Book in Logic Courses.- Introduction.- A Taste of Logic.- Everything All at Once and a Warning.- Statement Logic, Formal Languages, and Informal Arguments.- Valid Arguments, Convincing Arguments, and Punk Logic.- Predicates, Programs, and Antique Logic.- Deduction, Infinity, and a Haircut.- Symbolic Sophistication, Induction, and Business Logic.- Completeness, Disbelief, Debates, and Dinner.- Paradox, Impossibility, and the Law.- Notes.- References.- Hints.- Some Answers.- Index.

Real Analysis in Paraconsistent Logic

Abstract: This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open.