Abstract
In this paper we overview recent results about the lattice of subvarieties of the variety BL of BL-algebras and the equational definition of some families of them.
Similar content being viewed by others
References
Aglianó P, Ferreirim IMA, Montagna F Basic hoops: an algebriac study of continuous t-norms. Studia Logica (to appear)
Aglianó P, Montagna F (2003) Varieties of BL-algebras I: general properties. J Pure Appl Algebra 181:105–129
Belluce LP, Di Nola A, Lettieri A (1993) Local MV-algebras. Rend Circ Mat Palermo 42:347–361
Blok WJ, Ferreirim IMA (2000) On the structure of hoops. Algebra Universalis 43:233–257
Burris S, Sankappanavar HP (1981) A course in Universal Algebra, Graduate texts in Mathematics, Springer, Berlin Heidelberg New York
Busaniche M (2005) Decomposition of BL-chains. To appear in Algebra Universalis Vd. 52, Number 4, 519–525
Chang CC (1958) Algebraic analysis of many-valued logic. Trans Am Math Soc 88:467–490
Cignoli R, Esteva F, Godo L, Torrens A (2000) Basic fuzzy logic is the logic of continuous t-norms and their residua. Soft Computing 4:106–112
Cignoli R, D'Ottaviano IML, Mundici D (2000) Algebraic Foundations of Many-valued Reasoning, Kluwer, Doredrecht
Cignoli R, Torrens A (2000) An algebraic analysis of product logic. Mult Val Logic 5:45–65
Cignoli R, Torrens A (2003) Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic. Arch Math Logic 42:361–370
Di Nola A, Lettieri A (1994) Perfect MV-algebras are categorically equivalent to abelian ℓ-groups. Studia Logica 53:417–432
Di Nola A, Lettieri A (1999) Equational characterization of all varities of MV algebras. J Algebra 22:463–474
Di Nola A, Esteva F, Garcia P, Godo L, Sessa S (2002) Subvarieties of BL-algebras generated by single-component chains. Arch Math Logic 41:673–685
Di Nola A, Sessa S, Esteva F, Godo L, Garcia P (2002) The variety generated by perfect BL-algebras: an algebraic approach in a fuzzy logic setting. Ann Math Artif Intell 35:197–214
Esteva F, Godo L, Montagna F (2004) Equational Characterization of the Subvarieties of BL Generated by T-Norm Algebras Studia logica 76, 161–200
Ferreirim IMA (1992) On varieties and quasi varieties of hoops and their reducts. PhD Thesis, University of Illinois
Gispert J (2002) Universal classes of MV-chains with applications to many valued logics. Math Logic Q 48:581–601
Gispert J, Mundici D, Torrens A (1999) Ultraproducts of Z with an Application to Many-Valued Logics. J Algebra 219:214–233
Gottwald S (2001) A Treatise on Many-valued Logics. Studies in logic and computation, Research Studies Press, Baldock
Grigolia RS (1977) Algebraic Analysis of Lukasiewicz-Tarski's n-valued logical systems. In: Wojcicki AR, Malinowski G (eds) Selected papers on Lukasiewicz sentential calculus. Ossolineum, Wroclaw, pp 81–92
Hájek P (1998) Metamathematics of fuzzy logic. In: Trends in logic-studia logica library, vol 4. Kluwer, Dordercht/Boston/London
Hájek P (1998) Basic fuzzy logic and BL-algebras. Soft Computing 2:124–128
Haniková Z (2002) A note on propositional tautologies of individual continuous t-norms vol 12. Neural Netw World (5) 453–460
Hecht T, Katrinak T (1972) Equational classes of relative Stone algebras. Notre Dame J Formal Logic 13:248–254
Komori Y (1981) Super- Łukasiewicz implicational logics. Nagoya Math J 84:1119–133
Laskowski MC, Shashoua YV (2002) A classification of BL-algebras. Fuzzy Sets Syst 131:271–282
Mostert PS, Shields AL (1957) On the structure of semigroups on a compact manifold with boundary. Ann Math 65:117–143
Mundici D (1986) Interpretations of AFC*-algebras in Łukasiewicz sentential calculus. J Funct Anal 65:15–63
Panti G (1999) Varieties of MV algebras. J Appl Non-Classical Logic 9:141–157
Rodríguez AJ, Torrens A (1994) Wajsberg algebras and Post algebras. Studia Logica 53:1–19
Turunen E, Sessa S (2001) Local BL-algebras. Int J Multiple Valued Logic 6:229–249
Turunen E (1999) BL-algebras and fuzzy logic. Mathware and Soft Comput 1:49–61
Turunen E (2001) Boolean deductive systems of BL-algebras. Arch Math Logic 40:467–473
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Di Nola, A., Esteva, F., Godo, L. et al. Varieties of BL-algebras. Soft Comput 9, 875–888 (2005). https://doi.org/10.1007/s00500-004-0446-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-004-0446-8