Advertisement

Free BLΔ Algebras

  • Franco Montagna
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 11)

Abstract

We prove that the BL algebra consisting of the ordinal sum of n + 1 copies of the standard MV-algebra on [0,1] generates the variety generated by all n generated BL algebras.

Keywords

Fuzzy Logic Induction Hypothesis Free Algebra Algebraic Subset Basic Fuzzy Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AFM99]
    P. AGLIANÓ, I.M.A. FERREIRIM, F. MONTAGNA Basic hoops: an algebraic study of continuous t-norms, Preprint 1999.Google Scholar
  2. [AM00]
    P. Aglianó, F. Montagna Varieties of basic algebras,Preprint 2000.Google Scholar
  3. [BO]
    J. R. Buchi And Owens, Complemented monoids and groups,unpublished manuscript.Google Scholar
  4. [Ba96]
    M. Baaz: Infinite-valued Gödel logics with 0–1 projections and relativizations. In GODEL’96–Logical foundations of mathematics, computer science and physics. Lecture Notes in Logic 6 (1996), P. Hâjek ( Ed. ), Springer Verlag, pp. 23–33.Google Scholar
  5. [BF96]
    W.J. Blok, I.M.A. Ferreirim On the structure of hoops,to appear in Algebra Universalis.Google Scholar
  6. [BF93]
    W.J. Blok, I.M.A. Ferreirim, Hoops and their implicational reducts, Algebraic Logic, Banach Center pub. 28, Warsaw 1993.Google Scholar
  7. [BP94]
    W.J. Blok, D. Pigozzi, On the structure of varieties with equationally definable principal congruences III, Algebra Universalis 32, 545–608.Google Scholar
  8. [Ch58]
    C. C. Chang Algebraic analysis of many-valued logics, Trans Amer. Math. Soc. 88, 467–490.Google Scholar
  9. [Ch59]
    C. C. Chang A new proof of the completeness of Lukasiewicz axioms, Trans Amer. Math. Soc. 93, 74–80.Google Scholar
  10. [CEGT99]
    R. Cignoli, F. Eestva, L. Gono, A. Torrens, Basic fuzzy logic is the logic of continuous t-norms and their residua,to appear in Soft Computing.Google Scholar
  11. [COM95]
    R. Cignolic, I.M.L. D’Ottanviano, D. Mundici, Algebras das Logicas de Lukasiewicz, Centro de Logica, Epistemologia e Historia de Ciencia UNICAMP, 1995, Campinas, (Brazil).Google Scholar
  12. [CT98]
    R. Cignoli, A. Torrens, An algebraic analysis of Product Logic,to appear in Multiple-valued Logic.Google Scholar
  13. [H98]
    P. Hajek, Metamathematics of Fuzzy Logic, Kluwer, 1988.Google Scholar
  14. [Ha98]
    P. Hajek, Basic fuzzy logic and BL algebras, Soft Computing 2 (1998), 124–128.Google Scholar
  15. [MMT]
    R. Mackenzie, G. Mcnulty, W. Taylor, Algebras, Lattices, Varieties, Vol I, Wadsworth and Brooks/Cole, Monterey CA, 1987.Google Scholar
  16. [MN51]
    R. Mcnaughton, A theorem about infinite-valued sentential logic, Journ. Symb. Log. 16 (1951), 71–83.MathSciNetCrossRefGoogle Scholar
  17. [MP99]
    D. Mundici, Interpretation of AFC* algebras in Lukasiewicz sentential calculus, Journal of Functional Analysis, 65 (1986) 15–63.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Franco Montagna
    • 1
  1. 1.Dipartimento di MatematicaUniversitá di SienaSienaItaly

Personalised recommendations