Paraconsistent logic

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

Logics of Formal Inconsistency enriched with replacement: an algebraic and modal account

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.

Support at Decision in Electrical Systems of subtransmission through selection of Topologies by a Paraconsistent Simulator

Abstract: In this work, we present a Simulator Program that identifies the topologies and supports operation staff in decision-making about loads reassignments and changes in electric network, offering a selection of the best settings. Facing a contingency situation or action of relocation of electrical system of subtransmission lines, the Simulator considers the current state and uses special algorithms that detect the current network topology, interprets results and presents for operation the possible different maneuvers with their respective degrees of reliability. For these actions the software Simulator elaborates the states investigation of circuit breakers and electric keys, analysis of load flow, makes risk prediction and the mathematical analysis of remote sensing values. The software Simulator uses in some of his actions, special algorithms that are based on Paraconsistent Annotated Logic (PAL), which is a non-classical logic whose main property is to accept contradiction in their fundamentals. These algorithms based on PAL offer greater speed of processing and allows the Paraconsistent Simulator of topologies (ParaSimTop) to be implemented in real time.

Analytical tableaux for da Costa's hierarchy of paraconsistent logics Cn, 1≤n<ω

Abstract: In this paper we present a new hierarchy of analytical tableaux systems TNDC n, 1≤n<ω, for da Costa's hierarchy of propositional paraconsistent logics Cn, 1≤n<ω. In our tableaux formulation, we int...

Decidability and Undecidability in Probability Logic

Abstract: We study computational aspects of a probabilistic logic based on a well-known model of induction by Valiant. We prove that for this paraconsistent logic the set of valid formulas is undecidable.