Introduction to Many-Valued Logics
Fronhöfer B.
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.
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.