Metamathematics of Fuzzy Logic

1. Front Matter

   Pages N3-viii

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2. Preliminaries

   • Petr Hájek

   Pages 1-26

3. Many-Valued Propositional Calculi

   • Petr Hájek

   Pages 27-61

4. Łukasiewicz Propositional Logic

   • Petr Hájek

   Pages 63-87

5. Product Logic, Gödel Logic (and Boolean Logic)

   • Petr Hájek

   Pages 89-107

6. Many-Valued Predicate Logics

   • Petr Hájek

   Pages 109-147

7. Questions of Computational Complexity and Undecidability

   • Petr Hájek

   Pages 149-166

8. On Approximate Inference

   • Petr Hájek

   Pages 167-194

9. Generalized Quantifiers and Modalities

   • Petr Hájek

   Pages 195-248

10. Miscellanea

    • Petr Hájek

    Pages 249-276

11. Historical Remarks

    • Petr Hájek

    Pages 277-282

12. Back Matter

    Pages 283-299

    PDF

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.

• addition
• logic
• mathematical logic
• predicate logic

"...Moreover, it can be an excellent guideline for a postgraduate course in fuzzy logic because of its clear and well-organized content. Definitively, an excellent book that we enthusiastically recommend, and that fuzzy and mathematical logic (and probably philosophical logic as well) communities have been waiting for, for a long time."
(F. Esteva, L. Godo, International Journal of General Systems, 29:5 (2000)
"On whole this book occupies a unique place in the literature on fuzzy sets and fuzzy logic and fills a substantial gap. This is the only existing monograph offering a comprehensive study of triangular norms and their interconnections. Overall the book is very well written and should become the standard reference for triangular norms."
(Mathematical Reviews, 2002a)

• Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic

  Petr Hájek

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