Varieties of BL-algebras

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.

[1]  Yuichi Komori.  Super-Ł ukasiewicz implicational logics , 1978 .

[2]  W. Blok,et al.  On the structure of hoops , 2000 .

[3]  Lluis Godo,et al.  Basic Fuzzy Logic is the logic of continuous t-norms and their residua , 2000, Soft Comput..

[4]  Michael C. Laskowski,et al.  A classification of BL-algebras , 2002, Fuzzy Sets Syst..

[5]  Antoni Torrens Torrell,et al.  Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic , 2003, Arch. Math. Log..

[6]  Antonio di Nola,et al.  Subvarieties of BL-algebras generated by single-component chains , 2002, Arch. Math. Log..

[7]  Yuichi Komori.  Super-Łukasiewicz propositional logics , 1981, Nagoya Mathematical Journal.

[8]  Antonio di Nola,et al.  The Variety Generated by Perfect BL-Algebras: an Algebraic Approach in a Fuzzy Logic Setting , 2004, Annals of Mathematics and Artificial Intelligence.

[9]  Ada Lettieri,et al.  Equational characterization of all varieties of MV-algebras , 1999 .

[10]  Petr Hájek,et al.  Basic fuzzy logic and BL-algebras , 1998, Soft Comput..

[11]  D. Mundici.  Interpretation of AF -algebras in ukasiewicz sentential calculus , 1986 .

[12]  Petr Hájek,et al.  Basic fuzzy logic and BL-algebras II , 1998, Soft Comput..

[13]  E. Turunen.  BL-algebras of basic fuzzy logic , 1999 .

[14]  Joan Gispert,et al.  Universal Classes of MV-chains with Applications to Many-valued Logics , 2002, Math. Log. Q..

[15]  Giovanni Panti,et al.  Varieties of MV-algebras , 1999, J. Appl. Non Class. Logics.

[16]  Manuela Busaniche.  Decomposition of BL-chains , 2005 .

[17]  Antoni Torrens Torrell,et al.  Wajsberg algebras and Post algebras , 1994, Stud Logica.

[18]  Franco Montagna,et al.  Equational Characterization of the Subvarieties of BL Generated by t-norm Algebras , 2004, Stud Logica.

[19]  S. Gottwald.  A Treatise on Many-Valued Logics , 2001 .

[20]  P. Aglianò,et al.  Varieties of BL- algebras I: General properties. , 2003 .

[21]  D. Mundici,et al.  Algebraic Foundations of Many-Valued Reasoning , 1999 .

[22]  T. Hecht,et al.  Equational classes of relative Stone algebras , 1972, Notre Dame J. Formal Log..

[23]  Antonio di Nola,et al.  Perfect MV-algebras are categorically equivalent to abelianl-groups , 1994, Stud Logica.

[24]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[25]  C. Chang,et al.  Algebraic analysis of many valued logics , 1958 .

[26]  P. Mostert,et al.  On the Structure of Semigroups on a Compact Manifold With Boundary , 1957 .

[27]  Esko Turunen,et al.  Boolean deductive systems of BL-algebras , 2001, Arch. Math. Log..

[28]  Antoni Torrens Torrell,et al.  Ultraproducts of Z with an Application to Many-Valued Logics☆ , 1999 .