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A semantic analysis of some distributive logics with negation

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EN
Abstrakty
EN
In this paper we shall study some extensions of the semilattice based deductive systems S (N) and S (N; 1), where N is the variety of bounded distributive lattices with a negation op- erator. We shall prove that S (N) and S (N; 1) are the deductive systems generated by the local consequence relation and the global consequence relation associated with ¬-frames, respectively. Using algebraic and relational methods we will prove that S (N) and some of its extensions are canonical and frame complete.
Słowa kluczowe
Rocznik
Tom
Strony
81--100
Opis fizyczny
Bibliogr. 16 poz.
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autor
  • CONICET and Departamento de Matematicas, Facultad de Ciencias Exactas, Universidad Nacional del Centro Pinto 399 7000 Tandil. Argentina
Bibliografia
  • [1] F. Bou, F. Esteva, J. M. Font, A. Gil, L. Godo, A. Torrens, A., and V. Verdú, Logics preserving degrees of truth from varieties of residuated lattices, Journal of Logic and Computation 19 (2009), pp. 1031-1069.
  • [2] R. Ertola, M. Sagastume, Subminimal logic and weak algebras, Reports on Math. Logic 44 (2009), pp. 153-166.
  • [3] R. Dwinger and P.H. Balbes, Distributive Lattices, University of Missouri Press, Columbia, MO, 1974.
  • [4] P. Blackburn, M. de Rijke, Y. Venema, Modal Logic, Cambridge Tracts in Theoretical Computer Science 53, Cambridge University Press, 2001.
  • [5] S. A. Celani, Distributive lattices with a negation operator, Math. Logic Quarterly 45 (1999), pp. 207-218.
  • [6] S. A. Celani, Notes on the representation of distributive modal algebras, Miskolc Mathematical Notes 9:2 (2008), pp. 81-89.
  • [7] S A. Celani and L. M. Cabrer, Weak-quasi-Stone algebras, Math. Logic Quarterly 55:3 (2009), pp. 288-298.
  • [8] K. Dosén:. Negative modal operator in intuitionistic logic, Publications de L'Institut Mathematique (Beograd) (N.S) 35:49 (1984), pp. 3-14.
  • [9] K. Dosén, Negation as a modal operator, Reports on Mathematical Logic 20 (1986), pp. 15-27.
  • [10] J. Michael Dunn, C. Zhou, Negation in the Context of Gaggle Theory, Studia Logica 80:2-3 (2005), pp. 235-264.
  • [11] J. M. Font, On semilattice-based logics with an algebraizable assertional companion, Reports on Mathematical Logic 46 (2011), pp. 109-132.
  • [12] R. Jansana, Selfextensional Logics with a Conjunction, Studia Logica 84:1 (2006), pp. 63-104.
  • [13] S. P. Odintsov, Combining intuitionistic connectives and Routley negation, Siberian Electronic Mathematical Reports (2010), pp. 21-41.
  • [14] H. A. Priestley, Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. 3:24 (1972), pp. 507-530.
  • [15] N. A. Sankappanavar and H. P. Sankappanavar, Quasi-Stone algebras, Math. Logic Quarterly 39 (1993), pp. 255-268.
  • [16] Y. Shramko, Dual Intuitionistic Logic and a Variety of Negations. The Logic of Scientific Research, Studia Logica 80:2-3 (2005), pp. 347-367.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c525d86e-84d1-44bc-9a8c-f4ba078ef129
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