Introduction to Many-Valued Logics

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Internet-Publication. — 2011. — 388 (195) p. English. (Interactive menu).[Bertram Fronhöfer. Faculty of Computer Science. Technische Universität Dresden. August 4, 2011].Overview. Modern Pioneers of 3-Valued Logic.Prelude: Classical (Two-valued) Propositional Logic.History and Intuition of Many-Valued Logic.Kleene’s Strong 3-Valued Logic.Łukasiewicz’s 3-Valued Logic.Bochvar’s Internal 3-Valued Logic.Bochvar’s External 3-Valued Logic.Definability of Connectives.Interdefinability of Connectives.Defining Normal Connectives with Łukasiewicz 3-valued Logic.Defining Non-Normal Connectives.Łukasiewicz’s Bold Connectives.Non Truth Centered Semantical Concepts.Quasi-Tautologies.Quasi-Entailment.Example: Logic of Paradox.Degree Entailment.Derivation Systems for 3-Valued Propositional Logic.Prelude: A Derivation System for Classical Propositional Logic.An Axiomatic System for Łukasiewicz’s 3-Valued Logic.Completeness of 3-valued Łukasiewicz’s Logic.Application: Independence of Axioms.A Pavelka-Style Derivation System for Łukasiewicz Logic.Łukasiewicz Modalities.Gonseth's objection.Classical semantical contradiction. Concerning the ‘Original’ 2nd Axiom.1st axiom.2nd axiom.3rd axiom.Bibliography.