Poset Product and BL-Chains

Article
  • 16 Downloads

Abstract

Different constructions of BL-chains are compared. We establish when the ordinal sum and the poset product of the same family of BL-chains coincide. We also compare the poset product of MV-chains and product chains with saturated BL-chains.

Keywords

BL-algebras Ordinal sum Poset product Wajsberg hoops 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aglianò, P., and F. Montagna, Varieties of BL-algebras I: general properties, Journal of Pure and Applied Algebra 181: 105–129, 2003.CrossRefGoogle Scholar
  2. 2.
    Blok, W.J., and I.M.A. Ferreirim, On the structure of hoops, Algebra Universalis 43: 233–257, 2000.CrossRefGoogle Scholar
  3. 3.
    Busaniche, M., Decomposition of BL-chains, Algebra Universalis 52: 519–525, 2004.CrossRefGoogle Scholar
  4. 4.
    Busaniche, M., and F. Montagna, Hájek’s logic BL and BL-algebras, in Handbook of Mathematical Fuzzy Logic, vol. 1 of Studies in Logic, Mathematical Logic and Foundations, chap. V, College Publications, London, 2011, pp. 355–447.Google Scholar
  5. 5.
    Cignoli, R., I.M.L. D’Ottaviano, and D. Mundici, Algebraic Foundations of Many-Valued Reasoning, vol. 7 of Trends in Logic, Kluwer Academic Publishers, Dordrecht, 1999.Google Scholar
  6. 6.
    Cignoli, R., F. Esteva, L.L. Godo, and A. Torrens, Basic fuzzy logic is the logic of continuous t-norm and their residua, Soft Computing 4(2): 106–112, 2000.CrossRefGoogle Scholar
  7. 7.
    Davey, B.A., and H.A. Priestley, Introduction to lattices and order, 2 edn., Cambridge University Press, UK, 2002.CrossRefGoogle Scholar
  8. 8.
    Galatos, N., P. Jipsen, T. Kowalski, and H. Ono, Residuated lattices: an algebraic glimpse at substructural logics, vol. 151 of Studies in logic and the foundation of mathematics, Elsevier, Amsterdam, 2007.Google Scholar
  9. 9.
    Hájek, P., Basic fuzzy logic and BL-algebras, Soft Computing 2: 124–128, 1998.CrossRefGoogle Scholar
  10. 10.
    Hájek, P., Metamathematics of Fuzzy Logic, vol. 4 of Trends in Logic, Kluwer Academic Publishers, Dordrecht, 1998.CrossRefGoogle Scholar
  11. 11.
    Jipsen, P., Generalizations of boolean products for lattice-ordered algebras, Annals of Pure and Applied Logic 161: 228–234, 2009.CrossRefGoogle Scholar
  12. 12.
    Jipsen, P., and F. Montagna, On the structure of generealized BL-algebras, Algebra Universalis 55: 227–238, 2006.CrossRefGoogle Scholar
  13. 13.
    Jipsen, P., and F. Montagna, The Blok-Ferreirim theorem for normal GBL-algebras and its applications, Algebra Universalis 60: 381–404, 2009.CrossRefGoogle Scholar
  14. 14.
    Jipsen, P., and F. Montagna, Embedding theorems for classes of GBL-algebras, Journal of Pure and Applied Algebra 214: 1559–1575, 2010.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Instituto de Matemática Aplicada del Litoral UNL, CONICET, FIQCCT-CONICET-Santa FeSanta FeArgentina

Personalised recommendations