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Non canonicity of BL-algebras

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Języki publikacji
EN
Abstrakty
EN
In this work we study canoncity of BL-algebras and some of its subvarieties. We prove that the only subvarieties of Lp roduct sign G (see page 94) that are sigma-canonical and pi-canonical are the ones generated by finite families of finite algebras.
Słowa kluczowe
Rocznik
Tom
Strony
85--103
Opis fizyczny
Bibliogr. 16 poz., rys.
Twórcy
autor
  • CONICET and Departamento de Matem´aticas. Facultad de Ciencias Exactas Universidad Nacional del Centro Pinto 399 7000 Tandil. Argentina, cabrer@exa.unicen.edu.ar
Bibliografia
  • [1] R. L. Cignoli, A. Torrens, An algebraic analysis of product logic, Multiple valued Logic 5 (2000), pp. 45–65.
  • [2] A. Di Nola, F. Esteva, P. Garcia, L. Godo, S. Sessa, Subvarieties of BL-algebras generated by single-component chains, Archive for Mathematical Logic 41, 7 (2002),pp. 673–685.
  • [3] F. Esteva, L. Godo, Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy Sets and Systems 124, 3 (2001), pp. 271–288.
  • [4] M. Gehrke, J. Harding, Bounded lattice expansions, Journal of Algebra 238, 1 (2001),pp. 345–371.
  • [5] M. Gehrke, B. Jónsson, Bounded distributive lattices with operators, Mathematica Japonica 40, 2 (1994), pp. 207–215.
  • [6] M. Gehrke, B. Jónsson, Bounded distributive lattice expansions, Mathematica Scandinavica 94, 1 (2004), pp. 13–45.
  • [7] M. Gehrke, H. Priestley, Canonical extensions of double quasioperator algebras: An algebraic perspective on duality for certain algebras with binary operations, Journal of Pure and Applied Algebra 209, 1 (2007), pp. 269–290.
  • [8] M. Gehrke, H. Priestley, Non-canonicity of MV-algebras, Houston Journal of Mathematics 28, 3 (2002), pp. 449–455.
  • [9] P. Hájek, Basic fuzzy logic and BL-algebras, Soft Computing 2, 3 (1998), pp. 124–128.
  • [10] P, Hájek, Metamathematics of Fuzzy Logic, Trends in Logic - Studia Logica Library 4, Kluwer Academic Publishers (1998).
  • [11] P. Jipsen, C. Tsinakis, A Survey of Residuated Lattices, Ordered Algebraic Structures (2002), Kluwer Academic Publishers, pp. 19-56.
  • [12] B. Jónsson, A. Tarski, Boolean algebras with operators, American Journal of Mathematics 73 (1951), pp. 891–939.
  • [13] B. Jónsson, A. Tarski, Boolean algebras with operators II, American Journal of Mathematics 74 (1952), pp. 127–162.
  • [14] Y. Komori, Super- Lukasiewics propositional logics, Nagoya Mathematical Journal 84 (1981), pp. 119–133.
  • [15] H. Ono, Substructural logics and residuated lattices - an introduction, Trends in Logic 21 (2003), 50 Years of Studia Logica. Kluwer Academic Publishers, pp. 193–228.
  • [16] E. Turunen, Mathematics Behind Fuzzy Logic, Advances in soft Computing, Physica-Verlag, Heidelberg (1999).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ7-0007-0087
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