Basic many-valued logic

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Internet-Publication. — 48 p. English. (OCR-слой).[Alasdair Urquhart in Clarkson, Ontario (Canada). University of Toronto].Many-valued logic is a vast field with hundreds of published papers and numerous monographs devoted to it. I have attempted to keep this survey to manageable length by focusing on many-valued logic as an independent discipline. This means that such topics as the use of many-valued logics for proving the independence of axioms in propositional logic have been omitted.I am indebted to Gordon Beavers, Peter O’Hearn, Wolfgang Rautenberg and Andrzej Wro´nski for comments on the earlier version of this survey, and to Daniele Mundici for his constructive criticism of the revised version.ContentsEarly History and Motivation.Introduction.Lukasiewicz and Future Contingency.Lukasiewicz’s 3-valued Matrices and their Motivation.Other Lukasiewicz Logics.Post’s Many-valued Systems.Bochvar and the Paradoxes.Kleene’s System.General Theory of Many-valued Logics.The Matrix Method.Consequence Relations.The Bochvar Consequence Relation.The Kleene Consequence Relation.Lukasiewicz Consequence (Finite Case).Infinite-valued Consequence.Finite Axiomatizability.Definable Functions.Definable Functions in Lm.Characterizing Functional Completeness.Post Algebras.Generalized Post Algebras and Algorithmic Logic.Many-valued Predicate Logic.Set Theory in Many-valued Logic.Developments since 1960Model Structures on Commutative Monoids.Model Structures for Lω.Do Errors Add Up?Fuzzy Logic.The Logic of Significance.Retrospective.What is Many-valued Logic?The Logic of Uncertainty.‘Undefined’ as a Truth Value.Supervaluations.Summing Up.References (79 publ).