Skip to main content
SpringerLink
Log in

Extension of Łukasiewicz Logic by Product Connective

  • Conference paper
  • First Online:
Book cover Fuzzy Sets and Systems — IFSA 2003 (IFSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2715))

Included in the following conference series:

  • 1261 Accesses

The work of the first author was supported by the Czech Ministry of Education under project MSM 212300013, by the Grant Agency of the Czech Republic under project GACR 201/02/1540, by the Grant Agency of the Czech Technical University in Prague under project CTU 0208613, and by Net CEEPUS SK-042.

The work of the second author was supported by grant IAA1030004 of the Grant Agency of the Academy of Sciences of the Czech Republic.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

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.

References

  1. M. Baaz: Infinite-valued Gödel logic with 0-1 projector and relativisations. In Gödel’96: Logical foundations of mathematics, computer science and physics. Ed. P. Hájek, Lecture notes in logic 6:23–33, 1996.

    Google Scholar 

  2. R. Cignoli, I.M.L. D’Ottaviano, D. Mundici: Algebraic Foundations of Many-Valued. Reasoning. Kluwer, Dordrecht, 1999.

    Google Scholar 

  3. P. Cintula: The ŁΠ and ŁΠ1/2 propositional and predicate logics. Fuzzy Sets and Systems 124/3:21–34, 2001.

    Article  MathSciNet  Google Scholar 

  4. A. Di Nola, A. Dvurečenskij: Product MV-algebras. Multiple-Valued Logic 6:193–215, No.1–2, 2001.

    MATH  MathSciNet  Google Scholar 

  5. F. Esteva, L. Godo, F. Montagna: The ŁΠ and ŁΠ1/2 logics: two complete fuzzy. systems joining ŁLukasiewicz and product logics. Archive for Mathematical Logic 40:39–67, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  6. L. Fuchs: Partially Ordered Algebraic Systems. Pergamon Press, Oxford, 1963.

    MATH  Google Scholar 

  7. P. Hájek: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht, 1998.

    MATH  Google Scholar 

  8. M. Henriksen, J. R. Isbell: Lattice-ordered Rings and Function Rings. Pacific J. Math. 12:533–565, 1962.

    MATH  MathSciNet  Google Scholar 

  9. J. R. Isbell: Notes on Ordered Rings. Algebra Univ. 1:393–399, 1972.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. Łukasiewicz: O logice trojwartosciowej (On three-valued logic) Ruch filozoficzny 5:170–171, 1920.

    Google Scholar 

  11. V. Novák, I. Perfilieva, J. Močkoř: Mathematical Principles of Fuzzy Logic. Kluwer, Norwell, 1999.

    MATH  Google Scholar 

  12. J. Pavelka: On Fuzzy Logic I,II,III. Zeitschr. f. math. Logic und Grundlagen der Math. 25:45–52,119–134,447–464, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  13. G. Takeuti, S. Titani: Fuzzy Logic and Fuzzy Set Theory. Archive for Mathematical Logic 32:1–32, 1992.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Machine Perception, Dept. of Cybernetics, Faculty of Elec. Eng., Czech Technical University in Prague Technická 2, 166 27, Prague 6, Czech Republic

    Rostislav Horčík

  2. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 2, 182 07, Prague 8, Czech Republic

    Petr Cintula

  3. Dept. of Mathematics, FNSPE, Czech Technical University in Prague, Prague

    Petr Cintula

Authors
  1. Rostislav Horčík
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Petr Cintula
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Taner Bilgiç

  2. Dept. of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, 9000, Gent, Belgium

    Bernard De Baets

  3. Department of Electrical and Electronics Engineering, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Okyay Kaynak

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Horčík, R., Cintula, P. (2003). Extension of Łukasiewicz Logic by Product Connective. In: Bilgiç, T., De Baets, B., Kaynak, O. (eds) Fuzzy Sets and Systems — IFSA 2003. IFSA 2003. Lecture Notes in Computer Science, vol 2715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44967-1_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-44967-1_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40383-8

  • Online ISBN: 978-3-540-44967-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation