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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| Format: | eBook |
| Language: | English |
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Dordrecht
Springer Netherlands
1998, 1998
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| Edition: | 1st ed. 1998 |
| Series: | Trends in Logic, Studia Logica Library
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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