Paraconsistent logic

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

Ordinals in an Algebra-Valued Model of a Paraconsistent Set Theory

Abstract: This paper deals with ordinal numbers in an algebra-valued model of a paraconsistent set theory. It is proved that the collection of all ordinals is not a set in this model which is dissimilar to the other existing paraconsistent set theories. For each ordinal α of classical set theory α-like elements are defined in the mentioned algebra-valued model whose collection is not singleton. It is shown that two α-like elements (for same α) may perform conversely to validate a given formula of the corresponding paraconsistent set theory.

Paraconsistency in classical logic

Abstract: Classical propositional logic can be characterized, indirectly, by means of a complementary formal system whose theorems are exactly those formulas that are not classical tautologies, i.e., contradictions and truth-functional contingencies. Since a formula is contingent if and only if its negation is also contingent, the system in question is paraconsistent. Hence classical propositional logic itself admits of a paraconsistent characterization, albeit “in the negative”. More generally, any decidable logic with a syntactically incomplete proof theory allows for a paraconsistent characterization of its set of theorems. This, we note, has important bearing on the very nature of paraconsistency as standardly characterized.

Logics for Automated Reasoning in the Presence of Contradictions

Abstract: We basically discuss the adequacy of paraconsistent logics for knowledge representation. The specific problem being investigated, in a preliminary manner, is that of the formalization (by a logic) of reasoning in the presence of contradictions. In doing this, we examine various logical principles underlying some rival paraconsistent logics in order to provide indications for determining whether a particular paraconsistent logic is appropriate (in general or in special cases) for application to knowledge representation. We also argue in what way paraconsistent logics have advantages over other approaches to automated reasoning from inconsistent knowledge bases.

Many-valued logics and the logic of the C programming language

Abstract: In this paper we analyse the logic of the programming language C, where integers used as logical values. The classical logic has several axiom-systems, the oldest one is the axioms of the Boolean-algebra. We analyse how logical laws work in C. We also compare some many-valued systems to the logic of C. We show that the logic of C is not two-valued logic, neither a "classical many-valued logic". The commutative laws are not justified for all cases, because of the lazy evaluation of conditions. The problem occurs when an evaluation in a condition can produce error message. We present a three-valued non-commutative logic describing the logic of C.

Why Paraconsistent Logics

Abstract: In this chapter, we briefly review paraconsistent logics which are closely related to the topics in this book. We give an exposition of their history and formal aspects. We also address the importance of applications of paraconsistent logics to engineering.