Skip to main content
Log in

Arithmetical complexity of fuzzy predicate logics – a survey

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Results on arithmetical complexity of sets of tautologies and satisfiable formulas of various fuzzy logics (with respect to their standard t-norm based semantics as well as with respect to their general BL-algebra based semantics) are surveyed. Some new results are also obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aglianó P, Montagna F (2003) Varieties of BL-algebras I – general properties. J Pure Appl Algebra 181:105–129

    Google Scholar 

  2. Baaz M, Ciabattoni A, Fermüller C (2001) Herbrand's theorem for prenex Gödel logic and its consequences for theorem proving. Proceedings LPAR'2001 Lecture Notes in Computer in AI 2250, Springer, Berlin Heidelberg New York, pp 201–216

  3. Baaz M, Leitsch A, Zach R (1996) Incompleteness in an infinite-valued first order Gödel logic and of some temporal logics of programs. Proceedings CSL'95. Springer, Berlin Heidelberg New York, pp 1–15

  4. Cignoli R, Esteva F, Godo L, Torrens A (2000) Basic fuzzy logic is the logic of continuous t-norms and their residua. Soft Comput 4:106–112

    Google Scholar 

  5. Cignoli R, d'Ottaviano IML, Mundici D (2000) Algebraic foundations of many-valued reasoning. Kluwer Dordrecht

  6. Esteva F, Godo L (2001) Monoidal t-norm based logic: towards a logic for left-continuous t-norms. Fuzzy Sets Syst 124:271–288

    Google Scholar 

  7. Esteva F, Godo L, Hájek P, Montagna F (2003) Hoops and fuzzy logic. J Logic Computat 13:531–555

    Google Scholar 

  8. Esteva F, Godo L, Montagna F Axiomatization of any residuated fuzzy logic defined by a continuous t-norm (Preprint)

  9. Hájek P (1998) Metamathematics of fuzzy logic. Kluwer Dordrecht

  10. Hájek P (2001) Fuzzy logic and arithmetical hierarchy III. Studia Logica 68:129–142

    Google Scholar 

  11. Hájek P (2004) Fuzzy logic and arithmetical hierarchy IV. In: First-order revised (Hendricks et al., ed) Logos Verlag, 107–115

  12. Haniková Z (2002) A note on the complexity of propositional logics of individual t-algebras. Neural Netw World 5:441–452

    Google Scholar 

  13. Jenei S, Montagna F (2002) A proof of standard completeness for Esteva's and Godo's logic MTL, Studia logica 70:184–192

    Google Scholar 

  14. Montagna F (2001) Three complexity problems in quantified fuzzy logic. Studia logica 68:143–152

    Google Scholar 

  15. Montagna F (2005) On the predicate logics of continuous t-norm BL-algebras. Archive for Math Logic 44:97–114

    Google Scholar 

  16. Montagna F (2002) Ono H Kripke semantics, undecidability and standard completeness for Esteva and Godo's logic MTL∀. Studia Logica 71:199–206

    Google Scholar 

  17. Montagna F, Sacchetti L (2003) Kripke-style semantics for many-valued logics, Mathematical Logic Quarterly (A corrigendum to be published.)

  18. Mostowski A (1957) Axiomatizability of some many valued predicate calculi. Fund Math 44:165–190

    Google Scholar 

  19. Ragaz ME (1981) Arithmetische Klassifikation von Formelnmengen der unendlichwertigen Logik. ETH Zürich Thesis

  20. Rogers Jr H (1967) Theory of recursive functions and effective computability. McGraw-Hill, New York

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. Hájek.

Additional information

Partial support of the project LN00A056 (ITI) of Ministry of Education of the Czech Republic is recognized.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hájek, P. Arithmetical complexity of fuzzy predicate logics – a survey. Soft Comput 9, 935–941 (2005). https://doi.org/10.1007/s00500-004-0448-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-004-0448-6

Keywords

Navigation