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.Contents
Early 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 1960
Model 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).
