Preprint submitted to Elsevier Science. 8 May 2005. โ 56 p.
[Siegfried Gottwald: Institute of Logic and Philosophy of Science, Leipzig University, Leipzig, Germany].
The paper considers the fundamental notions of many-valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics.
Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics.
Basic ideas.From classical to many-valued logic.
Particular truth degree sets.
Designated truth degrees.
Logical validity and logical consequence.
Outline of the history.Basic Systems of Many-Valued Logics.The Gยจodel logics.
The Lukasiewicz logics.
The Product logic.
The Post logics.
Standard and Algebraic Semantics.Boolean algebras.
Godel and Lukasiewicz logics.
Product logic.
Post logics.
Particular Three- and Four-Valued Systems.Three-Valued Systems.
Four-Valued Systems.
Logics with T-Norm Based Connectives.Residuated Implications versus S-Implications.Continuous T-Norms.The Logic of Continuous T-Norms.The Logic of Left Continuous T-Norms.Some Generalizations.Pavelka Style Extensions.Gerlaโs General Approach.Some Recent Applications.Fuzzy sets theory.
Non-monotonic fuzzy reasoning.
References (150 publ).