Abstract
In this paper we investigate fuzzy propositional and first order logics which are complete or strongly complete with respect to a single chain, and we relate this properties with the existence of a universal chain for the logic.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aglianò P., Ferreirim I.M.A., Montagna F.: Basic hoops: An algebraic study of continuous t-norms. Studia Logica 87(1), 73–98 (2007)
Aglianò P., Montagna F.: Varieties of BL-algebras I: General properties. J. Pure Appl. Algebra 181, 105–129 (2003)
Bianchi, M., Montagna, F.: n-contractive BL logics, Preprint 2010, submitted
Blok W.J., Ferreirim I.M.A.: On the structure of hoops. Algebra Univers. 43, 233–257 (2000)
Blok, W., Pigozzi, D.: Algebraizable logics. Mem. Am. Math. Soc. 396, vol. 77, Am. Math. Soc., Providence (1989)
Burris S., Sankappanavar H.P.: A Course in Universal Algebra, Graduate Texts in Mathematics. Springer, New York (1981)
Cignoli R., D’Ottaviano M.I., Mundici D.: Algebraic Foundations of Many-valued Reasoning. Kluwer, Dordrecht (2000)
Cignoli R., Torrens A.: An algebraic analysis of product logic. Mult. Valued Log. 5, 45–65 (2000)
Cintula P.: Weakly implicative (fuzzy) logics I: Basic properties. Arch. Math. Log. 45(6), 673–704 (2006)
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. Log. 160(1), 53–81 (2009)
Cintula P., Hájek P.: On theories and models in fuzzy predicate logics. J. Symb. Log. 71(3), 863–880 (2006)
Di Nola A., Lettieri A.: Equational characterization of all varieties of MV-algebras. J. Algebra 221, 463–474 (1999)
Di Nola A., Lettieri A.: One chain generated varieties of MV-algebras. J. Algebra 25(2), 667–679 (2000)
Di Nola, A., Lenzi, G., Spada, L.: Representation of MV-algebras by regular ultrapowers, Technical Report 2009, to appear in Archive for Mathematical Logic
Esteva F., Godo L.: Monoidal t-norm based logic: Towards a logic for left-continuous t-norms. Fuzzy Set Syst. 124, 271–288 (2001)
Ferreirim, I. M. A.: On varieties and quasi varieties of hoops and their reducts. PhD thesis, University od Illinois at Chicago (1992)
Galatos N., Jipsen P., Kowalski T., Ono H.: Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Studies in Logic and the Foundations of Mathematics. Vol. 151, Elsevier, Amsterdam (2007)
Hájek P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)
Laskowski M., Malekpour S.: Provability in predicate product logic. Arch. Math. Log. 46, 365–378 (2007)
Montagna F.: Interpolation and Beth’s property in propositional many-valued logics: A semantic investigation. Ann. Pure Appl. Log. 141, 148–179 (2006)
Montagna F., Noguera C., Horčik R.: On weakly cancellative fuzzy logics. J. Log. Comput. 16, 423–450 (2006)
Mundici D.: Free products in the category of abelian ℓ-groups with strong unit. J. Algebra 113, 89–109 (1988)
Noguera C., Esteva F., Gispert J.: Triangular norm based axiomatic extensions of the weak Nilpotent minimum logic. Math. Log. Q. 54, 387–409 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Montagna, F. Completeness with respect to a chain and universal models in fuzzy logic. Arch. Math. Logic 50, 161–183 (2011). https://doi.org/10.1007/s00153-010-0207-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-010-0207-6