Skip to main content
Springer Nature Link
Log in

On Elementary Extensions in Fuzzy Predicate Logics

  • Conference paper
Computational Intelligence for Knowledge-Based Systems Design (IPMU 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6178))

  • 2057 Accesses

Abstract

Our work is a contribution to the model-theoretic study of equality-free fuzzy predicate logics. We give a characterization of elementary equivalence in fuzzy predicate logics using elementary extensions and introduce an strengthening of this notion, the so-called strong elementary equivalence. Using the method of diagrams developed in [5] and elementary extensions we present a counterexample to Conjectures 1 and 2 of [8].

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Baaz, M., Fermueller, C.G., Zach, R.: Arithmetical extensions of relational systems. Compositio Math. 13, 81–102 (1957)

    Google Scholar 

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

    Google Scholar 

  3. Cintula, P., Esteva, F., Gispert, J., Godo, L., Montagna, F., Noguera, C.: Distinguished algebraic semantics for t-norm based fuzzy logics: Methods and algebraic equivalencies. Ann. Pure Appl. Logic 160(1), 53–81 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cintula, P., Hájek, P.: Triangular norm based predicate fuzzy logics. Fuzzy Sets and Systems 161, 311–346 (2010)

    Article  MATH  Google Scholar 

  5. Dellunde, P.: Preserving mappings in fuzzy predicate logics(2009) (submitted)

    Google Scholar 

  6. Esteva, F., Godo, L.: Monoidal t-norm based logic: towards a logic for left-continuous t-norms. Fuzzy Sets and Systems 124(3), 271–288 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hájek, P.: Metamathematics of fuzzy logic. Trends in Logic-Studia Logica Library, vol. 4. Kluwer Academic Publishers, Dordrecht (1998)

    MATH  Google Scholar 

  8. Hájek, P., Cintula, P.: On theories and models in fuzzy predicate logics. The Journal of Symbolic Logic 71(3), 863–880 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Montagna, F.: Interpolation and beth’s property in propositional many-valued logics: A semantic investigation. Ann. Pure Appl. Logic 141(1-2), 148–179 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Novák, V., Perfilieva, I., Močkoř, J.: Mathematical principles of fuzzy logic. The Kluwer International Series in Engineering and Computer Science, vol. 517. Kluwer Academic Publishers, Boston (1999)

    MATH  Google Scholar 

  11. Tarski, A.: Der wahrheitsbegriff in den formalisierten sprachen. Studia Philosophica 1, 261–405 (1935)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Pilar Dellunde

  2. IIIA - CSIC, 08193, Bellaterra, Spain

    Pilar Dellunde & Francesc Esteva

Authors
  1. Pilar Dellunde
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesc Esteva
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str., 35032, Marburg, Germany

    Eyke Hüllermeier

  2. Fakultät Informatik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

  3. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität Dortmund, Otto-Hahn-Str. 4, 44227, Dortmund, Germany

    Frank Hoffmann

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dellunde, P., Esteva, F. (2010). On Elementary Extensions in Fuzzy Predicate Logics. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_76

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14049-5_76

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14048-8

  • Online ISBN: 978-3-642-14049-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics