Paraconsistent Logic: Consistency, Contradiction and Negation

Basel, Switzerland: Springer International Publishing (2016)
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Abstract

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses the history of paraconsistent logic; language, negation, contradiction, consistency and inconsistency; logics of formal inconsistency and the main paraconsistent propositional systems; many-valued companions, possible-translations semantics and non-deterministic semantics; paraconsistent modal logics; first-order paraconsistent logics; applications to information processing, databases and quantum computation; and applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning.

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Chapters

Matrices and Algebraizability

This chapter deals with matrices and algebraizability and their consequences, investigating in particular, the question of characterizability by finite matrices, as well as the algebraizability of mbC. Some negative results, in the style of the well-known Dugundji’s theorem for modal logics, are pro... see more

LFIs Based on Other Logics

This chapter is devoted to presenting an account of LFIs based on other logics, distinct from what was done in previous chapters, in which LFIs were based exclusively on positive classical logic. The chapter analyzes LFIs defined over other logical basis, such as positive intuitionistic logic, the f... see more

Some Extensions of mbC

This chapter deals with several extensions of mbC, which by its turn is a minimal extension of positive classical logic by means of a consistency operator and a paraconsistent negation. Important topics studied are consistency and inconsistency as derived connectives, inconsistency operators, as wel... see more

Semantics of Non-deterministic Character for LFIs

This chapter studies alternative semantics for the LFIs presented in previous chapters, concentrating on the novel notion of swap structures. The heritance of swap structures from M. Fidel’s notion of twist structures is evaluated, and the close relationship between the concepts of Fidel structures,... see more

Contradiction and (in)Consistency

Paraconsistency and Philosophy of Science: Foundations and Perspectives

This chapter examines the close connections between paraconsistency and philosophy of science, providing a philosophical justification for LFIs, and for paraconsistent logics in general, concluding that a paraconsistent approach to the foundations of science seem to be almost inevitable.

A Basic Logic of Formal Inconsistency: mbC

Paraconsistent Set Theory

This chapter offers a new approach to paraconsistent set theory by means of employing LFIs and their powerful consistency operator into sets, as well as into sentences. By assuming that not only sentences, but sets themselves can be classified as consistent or inconsistent objects, the basis for new... see more

First-Order LFIs

In the previous chapters, LFIs have been approached exclusively from the propositional viewpoint. This is justified by the fact that the main notions and issues of paraconsistency in general, and LFIs, in particular, occur at the propositional level, related to their main connectives, namely, paraco... see more

A Basic Logic of Formal Inconsistency: mbC

This chapter begins a formal study of Logics of Formal Inconsistency by offering a careful survey of the basic logic of formal inconsistency, mbC. The chapter also lays out the main notation, ongoing definitions and main ideas that will be used throughout the book.

Contradiction and Consistency

This chapter intends to clarify the whole project behind LFIs, explaining why and how contradiction and triviality cease to coincide, and why and how contradiction ceases to coincide with inconsistency. It also intends to explain that there is no opposition to the classical stance, besides the aware... see more

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Author Profiles

Marcelo E. Coniglio
University of Campinas
Walter Carnielli
University of Campinas

References found in this work

Protoalgebraic Logics.Janusz Czelakowski - 2003 - Studia Logica 74 (1):313-342.
Algebraizable Logics.W. J. Blok & Don Pigozzi - 2014 - Advanced Reasoning Forum.
Lectures on Propositional Calculi.Ryszard Wójcicki - 1984 - Pub. House of the Polish Academy of Sciences.

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