Paraconsistent logic

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

Philosophical applications of free logic

Abstract: Free logic, an alternative to traditional logic, has been seen as a useful avenue of approach to a number of philosophical issues of contemporary interest. In this collection, Karel Lambert, one of the pioneers in, and the most prominent exponent of, free logic, brings together a variety of published essays bearing on the application of free logic to philosophical topics ranging from set theory and logic to metaphysics and the philosophy of religion. The work of such distinguished philosophers as Bas van Fraassen, Dana Scott, Tyler Burge, and Jaakko Hintikka is represented. Lambert provides an introductory essay placing free logic in the logical tradition beginning with Aristotle, developing it as the natural culmination of a trend begun in the Port Royal logic of the 1600s, and continuing through current predicate logic--the trend to rid logic of existence assumptions. His Introduction also provides a useful systematic overview of free logic, including both a standard syntax and some semantical options.

Classical Negation and Expansions of Belnap---Dunn Logic

Abstract: We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion BD+ of four-valued Belnap---Dunn logic by classical negation. We show the expansion complete and maximal. Finally, we compare BD+ to some related systems found in the literature, specifically a four-valued modal logic of Beziau and the logic of classical implication and a paraconsistent de Morgan negation of Zaitsev.

A Logic of Multiple-Valued Argumentation

Abstract: This paper provides a new departure from the traditional two-valued argumentation frameworks. We address ourselves to formalize an expressive logic of argumentation, called a Logic of Multiple-valued Argumentation (LMA), on top of the very expressive knowledge representation language, called Extended Annotated Logic Programming (EALP), and examine its logical properties in various ways. EALP allows us to represent different kinds of uncertainty such as vagueness and inconsistency (or paraconsistency) in terms of multi-valuedness, and incompleteness with the help of default negation. LMA is a full-dress logic of argumentation in which agents can argue with other contenders, using multiple-valued knowledge base in terms of EALP.

Building a Knowledge Base System for an Integration of Logic Programming and Classical Logic

Abstract: This paper presents a Knowledge Base project for FO(ID), an extension of classical logic with inductive definitions. This logic is a natural integration of classical logic and logic programming based on the view of a logic program as a definition. We discuss the relationship between inductive definitions and common sense reasoning and the strong similarities and striking differences with ASP and Abductive LP. We report on inference systems that combine state-of-the-art techniques of SAT and ASP. Experiments show that FO(ID) model expansion systems are competitive with the best ASP-solvers.

Towards the unification of inconsistency handling mechanisms

Abstract: It is shown that the (flat) consequence relations defined from the Rescher-Manor Mechanism (that is: in terms of maximal consistent subsets of the premises) are all inconsistency-adaptive logics combined with a specific interpretation schema for the premises. Each of the adaptive logics is obtained by applying a suitable adaptive strategy to the paraconsistent logic CLuN. This result provides all those consequence relations with a (dynamic) proof theory and with a static (as well as a dynamic) semantics.