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 2013
TL;DR: Logics of proof and justification, nonmonotonic reasoning, logic in game theory and social software, and logical foundations of programming are reviewed.
Abstract: Constructive mathematics and type theory.- Logic, automata and automatic structures.- Computability and randomness.- Logical foundations of programming.- Logical aspects of computational complexity.- Logic programming and constraints.- Automated deduction and interactive theorem proving.- Logical methods in protocol and program verification.- Logical methods in program specification and extraction.- Domain theory logic.- Logical foundations of database theory.- Equational logic and term rewriting.- Lambda and combinatory calculi.- Categorical logic and topological semantics.- Linear logic.- Epistemic and temporal logics.- Intelligent and multiple agent system logics.- Logics of proof and justification.- Nonmonotonic reasoning.- Logic in game theory and social software.- Logic of hybrid systems.- Distributed system logics.- Mathematical fuzzy logic.- System design logics.
1 citations
TL;DR: In this article, the weakest LFI satisfying replacement, called RmbC, which is obtained from the basic LFI called mbC, is defined within the minimal bimodal non-normal logic E+E defined by the fusion of the nonnormal modal logic E with itself.
Abstract: It is customary to expect from a logical system that it can be algebraizable, in the sense that an algebraic companion of the deductive machinery can always be found. Since the inception of da Costa's paraconsistent calculi $C_n$, algebraic equivalents for such systems have been sought. It is known, however, that these systems are not self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, several systems belonging to this class of logics are only characterizable by semantics of a non-deterministic nature. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by extending with rules several LFIs weaker than $C_1$ , thus obtaining the replacement property (that is, such LFIs turn out to be self-extensional). Moreover, these logics become algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with additional operations. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied. In addition, a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. the proposed algebraic semantics.
1 citations
TL;DR: This paper shows the results of a sensing system for an autonomous mobile robot based on the paraconsistent neural network, which aims to inform the other robot components the obstacle position.
Abstract: This paper shows the results of a sensing system for an autonomous mobile robot. The sensing system is based on the paraconsistent neural network. The type of artificial neural network used in this work is based on the paraconsistent evidential logic (Eτ). The objective of the sensing system is to inform the other robot components the obstacle position. The reached results have been satisfactory.
1 citations
01 Jan 2016
TL;DR: It is argued that Carnap’s result that there are models of classical propositional logic with non-standard or non-normal interpretations of the connectives and that one kind of those interpretations violate the semantical principle of non-contradiction can be used.
Abstract: Given that, by definition, two statements are contradictories if and only if it is logically impossible for both to be true and logically impossible for both to be false, some authors have argued that the negation operators of certain paraconsistent logics are not “real” negations because they allow for a statement and its negation to be true together. In this paper we argue that the same kind of argument can be levelled against the negation operator of classical propositional logic. To this end, Carnap’s result that there are models of classical propositional logic with non-standard or non-normal interpretations of the connectives, and that one kind of those interpretations violate the semantical principle of non-contradiction which requires of a sentence and its negation that at least one of them be false can be used. We ponder the consequences of these arguments for the claims that paraconsistent negations are not genuine negations and that the negation of classical logic is a contradictory-forming operator and we consider the arguments that challenge the conflation between negation and contradiction.
1 citations
01 Jan 2016
TL;DR: This chapter analyzes LFIs defined over other logical basis, such as positive intuitionistic logic, the four-valued Belnap and Dunn’s logic, and some families of fuzzy logics.
Abstract: This chapter is devoted to presenting an account of LFIs based on other logics, distinct from what was done in previous chapters, in which LFIs were based exclusively on positive classical logic. The chapter analyzes LFIs defined over other logical basis, such as positive intuitionistic logic, the four-valued Belnap and Dunn’s logic, and some families of fuzzy logics.
1 citations