Paraconsistent logic

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

Paraconsistent inference from data using existential ω-entailment

Abstract: Existential Ω-entailment is a paraconsistent entailment relation designed to show the consequences of data which is inconsistent with a set of integrity constraints Ω. In this paper, we prove semantic properties of existential Ω-entailment and give an algorithm for computing it.

Logical space and the origins of pluralism in logic

Abstract: The fact that there is a plurality of systems that we call logics makes it requisite to attempt an explanation and thorough evaluation of the role of logic. I exploit the analogical development towards the pluralism of geometry to show that both disciplines are about some kinds of space which they explicate and that we can choose with some freedom the tools for engaging in an enterprise of these disciplines. After revisiting the development of non-classical (i.e. non-Euclidian) geometries, I present logical expressivism, as coined by Robert Brandom, and, returning again to geometry, show that an analogous doctrine of geometrical expressivism can also provide a viable account of the nature and purpose of the discipline and the reasons for plurality of both geometries and logics.

Common-sense reasoning in constructive discursive logic

Abstract: We consider common-sense reasoning in constructive discursive logic, which is a constructive version of Jaskowski's discursive logic. We discuss two problems in common-sense reasoning, i.e., paraconsistent and non-monotonic reasoning. First, we show that the logic can formalize paraconsistent reasoning, which can be inconsistent but nontrivial. Second, we argue that the logic can be used to express non-monotonic reasoning, in which old conclusions can be invalidated by new information. We also suggest future problems related to the proposed logic.

Relevance Logic as a Conservative Extension of Classical Logic

Abstract: Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe, then another perspective emerges: the theses of relevance logic, specifically the system R, may also be seen as the output of a conservative extension of the relation of classical consequence. We describe two ways in which this may be done. One is by defining a suitable closure relation out of the set of theses of relevance logic; the other is by adding to the usual natural deduction system for it further rules with ‘projective constraints’, whose application restricts the subsequent application of other rules. The significance of the two constructions is also discussed.

Tableau systems for paraconsistency and minimal inconsistency

Abstract: In this paper, the semantics of a paraconsistent logic and its nonmonotonic extension by minimal inconsistency are presented first. And then signed tableaux for paraconsistent logic and minimal tableaux for logic of minimal inconsistency is proposed. Finally, the reduction of logic of paraconsistency and minimal inconsistency on ordinary semantics which provides new approach to proof procedure and implementation of paraconsistency and minimal inconsistency are provided.