عنوان

Metamathematics of Fuzzy Logic

9781402003707

9789401153003

dltt

Metamathematics of Fuzzy Logic

[Book]

by Petr Hájek.

Dordrecht :

Imprint: Springer,

1998.

Trends in Logic, Studia Logica Library,

4

1572-6126 ;

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 -- 2.4 Some additional topics -- 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.

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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 imprecise (vague) propositions does have well-developed formal foundations and that most things usually named `fuzzy inference' can be naturally understood as logical deduction.

9781402003707

Springer eBooks

Logic, Symbolic and mathematical.

Logic.

Philosophy (General).

Hájek, Petr.

SpringerLink (Online service)

20190307155600.0

[Book]

Y