Topic
Paraconsistent logic
About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, proof systems for Nelson's paraconsistent logic N4 are comprehensively studied and some basic theorems including cut-elimination, normalization and completeness are uniformly proved using various embedding theorem.
48 citations
TL;DR: A novel approach to paraconsistent reasoning, that is, to reasoning from inconsistent information, is presented by renaming all literals occurring in the theory by introducing progressively formal equivalences linking the original literals to their renamings.
Abstract: We present a novel approach to paraconsistent reasoning, that is, to reasoning from inconsistent information. The basic idea is the following. We transform an inconsistent theory into a consistent one by renaming all literals occurring in the theory. Then, we restore some of the original contents of the theory by introducing progressively formal equivalences linking the original literals to their renamings. This is done as long as consistency is preserved. The restoration of the original contents of the theory is done by appeal to default logic. The overall approach provides us with a family of paraconsistent consequence relations.
Our approach is semantical because it works at the level of the propositions; it deals with the semantical link between a proposition and its negation. The approach is therefore independent of the combination of the connectives that are actually applied to the propositions in order to form entire formulas.
48 citations
TL;DR: This work presents a generalisation of the relational data model based on a 4-valued paraconsistent logic and defines algebraic operators that are generalisations of the usual operators, such as union, selection, join, on ordinary relations for this model.
Abstract: We present a generalisation of the relational data model based on a 4-valued paraconsistent logic. Our data model is capable of manipulating incomplete as well as inconsistent information. For this model, we define algebraic operators that are generalisations of the usual operators, such as union, selection, join, on ordinary relations. Our data model can underlie any database management system that deals with incomplete or inconsistent information. As another application of our model and its algebra, we present a bottom-up method for constructing the weak well-founded model of general deductive databases. This method can be very simply extended to construct the well-founded model.
47 citations
Journal Article•
47 citations
TL;DR: The nontriviality of the set theory so formulated is demonstrated, some elementary properties of this system of sets are deduced, and some of the problems of this approach are delineated.
Abstract: Recently there has been much interest in naive set theory in nonstandard logics. This note continues this trend by considering a set theory with a general comprehension schema based on the paraconsistent logic LP. We demonstrate the nontriviality of the set theory so formulated, deduce some elementary properties of this system of sets, and also delineate some of the problems of this approach.
47 citations