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2006 | 4 | 4 | 600-623
Tytuł artykułu

Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras

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EN
Abstrakty
EN
In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space.
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
4
Strony
600-623
Opis fizyczny
Daty
wydano
2006-12-01
online
2006-12-01
Twórcy
Bibliografia
  • [1] R. Dwinger and P.H. Balbes: Distributive Lattices, University of Missouri Press, Columbia, M, 1974.
  • [2] S.A. Celani: “Distributive lattices with fusion and implication”, Southeast Asian Bull. Math., Vol. 28, (2004), pp. 999–1010.
  • [3] S.A. Celani and R. Jansana: “Bounded Distributive lattices with Strict Implication”, Math. Log. Quart., Vol. 51(3), (2005), pp. 219–246. http://dx.doi.org/10.1002/malq.200410022
  • [4] R. Cignoli, I.M.L. D’Ottaviano and D. Mundici: Algebraic Foundations of Many-Valued Reasoning, Trends in Logic, Vol. 7, Kluwer Academic Publishers, 2000.
  • [5] R. Cignoli, F. Esteba, L. Godo and F. Montagna: “On a class of left continuous t-norms”, Fuzzy Set. Syst., Vol. 131, (2002), pp. 283–296. http://dx.doi.org/10.1016/S0165-0114(01)00215-9
  • [6] F. Esteba and L. Godo: “Monoidal t-norm based logic: towards a logic for left continuous t-norms”, Fuzzy Set. Syst., Vol. 124, (2001), pp. 271–288. http://dx.doi.org/10.1016/S0165-0114(01)00098-7
  • [7] M. Gehrke and H.A. Priestley: “Non-canonicity of MV-algebras”, Houston J. Math., Vol. 28(3), (2002), pp. 449–455.
  • [8] J.B. Hart, L. Rafter and C. Tsinakis: “The Structure of Commutative Residuated Lattices”, Int. J. Algebr. Comput., Vol. 12(4), (2002), pp. 509–524. http://dx.doi.org/10.1142/S0218196702001048
  • [9] P. Jipsen and C. Tsinakis: A Survey of Residuated Lattices, Ordered Algebraic Structures, Kluwer Academic Publishers, Dordrecht, 2002, pp. 19–56.
  • [10] N.G. Martinez: “A topological duality for some lattice oredered algebraic structures including l-groups”, Algebra Univ., Vol. 31, (1996), pp. 516–541. http://dx.doi.org/10.1007/BF01236503
  • [11] N.G. Martinez: “A simplified duality for implicative lattces and l-groups”, Studia Log., Vol. 56, (1994), pp. 185–204. http://dx.doi.org/10.1007/BF00370146
  • [12] N.G. Martinez and H.A. Priestley: “On Priestley spaces of lattice-ordered algebraic structures”, Order, Vol. 15 (1998), pp. 297–323. http://dx.doi.org/10.1023/A:1006224930256
  • [13] H.A. Priestley: “Ordered topological spaces and the representation of distributive lattices”, Proc. London Math. Soc., Vol. 24, (1972), pp. 507–530.
  • [14] H.A. Priestley: “Stone Lattices: a topological approach”, Fund. Math., Vol. 84, (1974), pp. 127–143.
  • [15] V. Sofronie-Stokkermans: “Duality and canonical extensions of bounded distributive lattices with operators, and applications to the semantics of non-classical logics I”, Studia Log., Vol. 64, (2000), pp. 93–132. http://dx.doi.org/10.1023/A:1005298632302
  • [16] V. Sofronie-Stokkermans: “Duality and canonical extensions of bounded distributive lattices with operators, and applications to the semantics of non-classical logics II”, Studia Log., Vol. 64, (2000), pp. 151–192. http://dx.doi.org/10.1023/A:1005228629540
  • [17] V. Sofronie-Stokkermans: “Resolution-based decision procedures for the universal theory of some classes of distributive lattices with operators”, J. Symb. Comput., Vol. 36, (2003), pp. 891–924. http://dx.doi.org/10.1016/S0747-7171(03)00069-5
  • [18] A. Urquhart: “Duality for Algebras of Relevant Logics”, Studia Log., Vol. 56, (1996), pp. 263–276. http://dx.doi.org/10.1007/BF00370149
  • [19] M. Ward and R.P. Dilworth: “Residuated lattices”, Trans. Amer. Math. Soc., Vol. 45, (1939), pp. 335–354. http://dx.doi.org/10.2307/1990008
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-006-0025-6
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