Paraconsistent Logic: Consistency, Contradiction and Negation

✍ Scribed by Walter Carnielli, Marcelo Esteban Coniglio (auth.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 417
• Series: Logic, Epistemology, and the Unity of Science 40
• Edition: 1
• Category: Library

✦ Synopsis

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 (i) the history of paraconsistent logic; (ii) language, negation, contradiction, consistency and inconsistency; (iii) logics of formal inconsistency (LFIs) and the main paraconsistent propositional systems; (iv) many-valued companions, possible-translations semantics and non-deterministic semantics; (v) paraconsistent modal logics; (vi) first-order paraconsistent logics; (vii) applications to information processing, databases and quantum computation; and (viii) applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning.

✦ Table of Contents

Front Matter....Pages i-xxiv
Contradiction and (in)Consistency....Pages 1-28
A Basic Logic of Formal Inconsistency: mbC ....Pages 29-62
Some Extensions of mbC....Pages 63-120
Matrices and Algebraizability....Pages 121-170
LFIs Based on Other Logics....Pages 171-236
Semantics of Non-deterministic Character for LFIs....Pages 237-291
First-Order LFIs....Pages 293-343
Paraconsistent Set Theory....Pages 345-367
Paraconsistency and Philosophy of Science: Foundations and Perspectives....Pages 369-389
Back Matter....Pages 391-398

✦ Subjects

Logic;Epistemology