### Metamathematics of Fuzzy Logic

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of impreci...

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Main Author: eBook English Dordrecht Springer Netherlands 1998, 1998 1st ed. 1998 Trends in Logic, Studia Logica Library Springer Book Archives -2004 - Collection details see MPG.ReNa
• One / Preliminaries
• 1.1 Introduction
• 1.2 A survey of Boolean propositional logic
• 1.3 Boolean predicate calculus
• 1.4 Function symbols; varieties of algebras
• 1.5 Lattices and Boolean algebras
• 1.6 Ordered Abelian groups
• Two / Many-valued propositional calculi
• 2.1 Continuous t-norms and their residua
• 2.2 The basic many-valued logic
• 2.3 Residuated lattices; a completeness theorem
• Three / ?ukasiewicz propositional logic
• 3.1 Getting ?ukasiewicz logic
• 3.2 MV-algebras; a completeness theorem
• 3.3 Rational Pavelka logic
• Four / Product logic, Gödel logic
• 4.1 Product logic
• 4.2 Gödel logic
• 4.3 Appendix: Boolean logic
• Five / Many-valued predicate logics
• 5.1 The basic many-valued predicate logic
• 5.2 Completeness
• 5.3 Axiomatizing Gödel logic
• 5.4 ?ukasiewicz and product predicate logic
• 5.5 Many-sorted fuzzy predicate calculi
• 5.6 Similarity and equality
• Six / Complexity and undecidability
• 6.1 Preliminaries
• 6.2 Complexity of fuzzy propositional calculi
• 6.3 Undecidability of fuzzy logics
• Seven / On approximate inference
• 7.1 The compositional rule of inference
• 7.2 Fuzzy functions and fuzzy controllers
• 7.3 An alternative approach to fuzzy rules
• Eight / Generalized quantifiers and modalities
• 8.1 Generalized quantifiers in Boolean logic
• 8.2 Two-valued modal logics
• 8.3 Fuzzy quantifiers and modalities
• 8.4 On “probably” and “many”
• 8.5 More on “probably” and “many”
• Nine / Miscellanea
• 9.1 Takeuti-Titani fuzzy logic
• 9.2 An abstract fuzzy logic
• 9.3 On the liar paradox
• 9.4 Concluding remarks
• Ten / Historical remarks
• 10.1 Until the forties
• 10.2 The fifties
• 10.3 The sixties
• 10.4 The seventies
• 10.5 The eighties
• 10.6 The nineties
• References