Introduction to Many-Valued Logics

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.