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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. .

Philosophy. --- Epistemology. --- Logic. --- Knowledge, Theory of. --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Epistemology --- Theory of knowledge --- Mental philosophy --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Humanities --- Methodology --- Genetic epistemology. --- Developmental psychology --- Knowledge, Theory of

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This volume is a collection of essays related to the work of Professor Yuriy Vasilievich Ivlev, a distinguished Russian logician and philosopher renowned for his expertise in many-valued and modal logics. Notably, his groundbreaking work on quasi-matrices for logics, now recognized as non-deterministic matrices and non-deterministic semantics, emerged in the 1970s. From a philosophical standpoint, Ivlev’s research delves into the formal analysis of indeterminacy, offering a logical framework to understand how sequences of indeterminate events can yield determinate outcomes. The volume follows two complementary lines of research. Firstly, it serves as a platform for the exploration and discussion of Ivlev’s seminal contributions to the algebraic characterization of both normal and non-normal modal logics, aimed at making these insights accessible to an international audience. Secondly, it features contributions from esteemed logicians and philosophers worldwide, offering diverseperspectives on the logical analysis of indeterminacy. This comprehensive volume will appeal to scholars and researchers in logic, philosophy, and mathematics who are engaged in the study of many-valued and modal methodologies for modeling situations of indeterminacy.

Logic. --- Philosophy. --- Mathematics. --- Computer science. --- Computer Science.