About the Book
The present book discusses all aspects of paraconsistent logic, including the latest findings, and its various systems. It includes papers by leading international researchers, which address the subject in many different ways: development of abstract paraconsistent systems and new theorems about them; studies of the connections between these systems and other non-classical logics, such as non-monotonic, many-valued, relevant, paracomplete and fuzzy logics; philosophical interpretations of these constructions; and applications to other sciences, in particular quantum physics and mathematics. Reasoning with contradictions is the challenge of paraconsistent logic. The book will be of interest to graduate students and researchers working in mathematical logic, computer science, philosophical logic, linguistics and physics.
Table of Contents:
C. Baskent: Game Semantics and
Paraconsistency.- D. Batens: Some
adaptive contributions to Logics of Formal Inconsistency.- Jean-Yves Beziau
and A. Franceschetto: Strong
Three-Valued Paraconsistent Logics.- R. C. Ertola B. Rodriguez and C.
Noguera I. lofent: Paraconsistent
degree-preserving fuzzy logic.- B. Brown: Symmetrical
Preservation Relations and Cognitive Commitments.- C. C. Caret Game
Semantics and Paraconsistency.- N. da Costa and C. de Ronde: Quantum Physics and Paraconsistency.- V.
Degauquier: A unified proof-theoretic approach of partial
and paraconsistent three-valued logics.- S. Dutta: Consequence
and Inconsistency: Paraconsistent Logics.- E. Ficara:Negation
and the Metaphysical Foundations of Logic.- H. Field: Restricted
Quantification in Paraconsistent and Other Nonclassical Logics.- D.
Gangopadhyay: Unscrambling the ‘Copenhagen omelet’ in
paraconsistent term.- P. Greenough: Going Glutty, Staying Classical.- C.
Heunen: Combining logical viewpoints in quantum theory.- R.
I. Ingalalli: Consistency in Indian Logic.- T. Jarmuzek: Tableau
metatheory for paraconsistent logics defined by possible world's semantics.- P.
Jetli: Aristotle’s Syllogistic Logic is a
Paraconsistent Logic.- H. Kurokawa: Hypersequent Calculi for
Dual-superintuitionstic Logics and an Extension of the Logic Cube.- O.
Korkmaz: A paraconsistent solution to Kratzer’s modal
semantics.- H. Omori: Naive set theories based on
expansions of BD enriched by classical negation.- A.
Moretti and R. Pélissier: Many-valuedness and paraconsistency
in a 3-oppositional quadrisimplex of sheaves.- C.
Mortensen: Wedge Sum as Inconsistent.- A.
Pietruszczak and M. Nasieniewski: Modal logics connected to Jaskowski's
logic D2.- G. Priest: The Adventures of the Catuskoti.- G.
Pulcini: Towards a unified setting for non-monotonicity
and paraconsistency.- V. Puncochár:Internal
and External logics of Nelson Models.- F. Putte: Adaptive Logics and Selection
Function.- D. Skurt: Iterated preferential models as a
strategy to make many-valued paraconsistent logics non-monotonic.- S.
Tarafder and M. Chakraborty: The Logic LS3 and its Comparison with
other Three-Valued Paraconsistent Logics.- E. Turunen: Two Paraconsistent Semantics for
Pavelka's Fuzzy Logic.- M. Vacek: Paraconsistency and Impossible
Worlds.- P. Verdée:Paraconsistent
and classical negation in the context of relevant implication.- D.
Zaitsev: Propositions, Paraconsistency, Paracompleteness.
About the Author :
JEAN-YVES BEZIAU, former PhD student of Newton da Costa, is professor at
the University of Brazil, Rio de Janeiro, and editor-in-chief of Logica
Universalis (Springer’s journal). He has done research around the world—France,
Brazil, Poland, Switzerland and California—and has launched two series of
international events: UNILOG, World Congress and School on Universal Logic;
SQUARE, World Congress on the Square of Opposition. He is the logic part
editor of the Internet Encyclopedia of Philosophy, joint project with Enyclopyedia
of Logic that he is editing.
MIHIR KUMAR CHAKRABORTY, PhD, a formerly professor
of pure mathematics and logic at the University of Calcutta, is visiting
professor at the School of Cognitive Sciences, Jadavpur University, and
director of Sivatosh Mookerjee Centre of Sciences, Kolkata. He also had
research assignments in Poland, France, Canada, Australia, Italy, Germany and
China. Professor Chakraborty had been visiting professor at the Centre for Soft
Computing Research, Indian Statistical Institute, Kolkata; Institute for Logic
Language and Cognition, Sun Yat-Sen University, Guangzhou, China; Institut de
Recherche en Informatique de Toulouse, University Paul Sabataire, Toulouse,
France; University of Paris VIII, France; University of Wollongong, Australia;
University of Regina, Canada; National Institute of Advanced Studies,
Bangalore, India; and Visva-Bharati, Santiniketan, India. A recipient of the
Deutscher Akademischer Austuasch Dienst fellowship, IISc fellowship, and
fellowship of West Bengal Academy of Sciences, Professor Chakraborty is member
of the Council and Research Project Committee of Indian Council for
Philosophical Research, and guest professor at the South West University of Chongqing,
China. He has about 150 research papers to his credit in several international
journals and edited volumes, co-authored one book A Geometry of Approximation (Springer),
authored three books in vernacular Bengali on philosophy of mathematics, and
co-edited several scientific publications. A member of the editorial board of
several international journals and a book series Logic in Asia: Studia Logic Library (Springer), Professor
Chakraborty’s areas of research are non-standard logics, rough set theory, fuzzy
set theory, reasoning in uncertainty and vagueness, logic of diagrams,
topology/functional analysis, and philosophy of mathematics. He also supervised
16 PhD students. Professor Chakraborty is founder of Calcutta Logic Circle,
Association for Logic in India, Indian Society for Fuzzy Mathematics and
Information Processing and member of the advisory board of International Rough
Set Society and Indian Rough Set Society.
SOMA DUTTA did her master and doctoral research at
the Department of Pure Mathematics, University of Calcutta, India. Her doctoral
research is about a theory of graded consequence, a field of study closely
related to fuzzy logic, initiated by her PhD supervisor Mihir Kumar
Chakraborty. Her research interests also include paraconsistent logics and
generalized quantifiers. She has been associated with The Institute of
Mathematical Sciences, Chennai, India, as a postdoctoral fellow. Presently, she
has a fellowship of European Research Consortium for Informatics and
Mathematics (ERCIM) to pursue postdoctoral research at the Faculty of
Mathematics, Informatics and Mechanics, University of Warsaw, Poland.
