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 article, the authors describe a procedure for developing models and associated proof systems for two styles of paraconsistent logic with negation and give an Urquhart-style representation of bounded not necessarily discrete lattices using (grill, cogrill) pairs.
Abstract: In this paper we describe a procedure for developing models and associated proof systems for two styles of paraconsistent logic. We first give an Urquhart-style representation of bounded not necessarily discrete lattices using (grill, cogrill) pairs. From this we develop Kripke semantics for a logic permitting 3 truth values: true, false and both true and false. We then enrich the lattice by adding a unary operation of negation that is involutive and antimonotone and show that the representation may be extended to these lattices. This yields Kripke semantics for a nonexplosive 3-valued logic with negation.
1 citations
•
01 Jan 2005
TL;DR: This paper uses a paraconsistent logic (LFI1) as the underlying logic for the specification of P-Datalog, a deductive query language for databases containing inconsistent information and presents a declarative semantics which captures the desired meaning of a recursive query executed over a database containing inconsistent facts.
Abstract: When integrating data coming from multiple different sources we are faced with the possibility of inconsistency in databases. A paraconsistent approach for knowledge base integration allows keeping inconsistent information and reasoning in its presence. In this paper, we use a paraconsistent logic (LFI1) as the underlying logic for the specification of P-Datalog, a deductive query language for databases containing inconsistent information. We present a declarative semantics which captures the desired meaning of a recursive query executed over a database containing inconsistent facts and whose rules allow infering information from inconsistent premises. We also present a bottom-up evaluation method for P-Datalog programs based on an alternating fixpoint operator.
1 citations
••
22 Sep 2010TL;DR: It is shown that the modified logic is classically sound and that its embedding into classical \(\mathcal{SROIQ}\) is consequence preserving, and inserting special axioms into a knowledge base allows additional nontrivial conclusions to be drawn, without affecting paraconsistency.
Abstract: The four-valued paraconsistent logic \(\mathcal{SROIQ}4\), originally presented by Ma and Hitzler, is extended to incorporate additional elements of \(\mathcal{SROIQ}\). It is shown that the modified logic is classically sound and that its embedding into classical \(\mathcal{SROIQ}\) is consequence preserving. Furthermore, inserting special axioms into a \(\mathcal{SROIQ}4\) knowledge base allows additional nontrivial conclusions to be drawn, without affecting paraconsistency. It is also shown that the interaction of nominals and cardinality restrictions prevents some \(\mathcal{SROIQ}4\) knowledge bases from having models. For such knowledge bases, the logic remains explosive.
1 citations
••
01 Jan 2000TL;DR: In this paper, it has been shown that Peirce's gamma part of his Existential Graphs (EG) contains that kind of treatment of modal logic that is today called model-theoretic.
Abstract: It has been recognized that Peirce’s gamma part of his Existential Graphs (EG) contains that kind of treatment of modal logic that is today called model-theoretic. Peirce is even supposed to have anticipated possible-worlds-semantics (PWS).1 In this paper I want to explore how close he got to our contemporary semantics for modal logics and if the differences one finds can only be seen as evidence of an archaic and outdated understanding of logical matters or if they have a hidden potential that might be fruitfully applied in the discussions of problems within the now dominant interpretation of logic.
1 citations
••
TL;DR: It is shown that the particular choose of exactly seven neutrosophic logical values has an interesting interpretation in terms of ancient Jaina logic (which has been developed centuries ago in India to deal with imprecise knowledge and the matter of paraconsistency).
Abstract: The aim of this paper is to introduce the concept of heptapartitioned neutrosophic soft set and to study some of its basic properties. This kind of set can be considered as a significant extension of the idea of neutrosophic set. In general, our research is based on the earlier study presented by Radha and Stanis Arul Mary in 2021. However, we combine their initial definition with the inspiring notion of soft set (which has been established by Molodtsov in 1999). We examine algebraic operations on our sets. Then we show that the particular choose of exactly seven neutrosophic logical values has an interesting interpretation in terms of ancient Jaina logic (which has been developed centuries ago in India to deal with imprecise knowledge and the matter of paraconsistency). Moreover, we exhibit some other potential practical applications of our theoretical concept. For example, it can be applied in widely understood social sciences.
1 citations