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Tytuł artykułu

Discrete Dualities for Heyting Algebras with Operators

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Języki publikacji
EN
Abstrakty
EN
Discrete dualities are presented for Heyting algebras with various modal operators, for Heyting algebras with an external negation, for symmetric Heyting algebras, and for Heyting-Brouwer algebras.
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Rocznik
Strony
275--295
Opis fizyczny
bibliogr. 24 poz.
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autor
Bibliografia
  • [1] Bezhanishvili, G., Varieties of monadic Heyting algebras, Part I Studia Logica 61 (3), 1998, 367-402; Part II Studia Logica 62 (1), 1999, 21-48.
  • [2] Celani,S. A., Jansana, R.: Priestley Duality, a Sahlqvist Theorem and a Goldblatt-Thomason Theorem for Positive Modal Logic. Logic Journal of the IGPL 7 (6), 1999, 683-715.
  • [3] Davey, B.A. and H.A. Priestley. [1990]. Introduction to Lattices and Order. Cambridge: Cambridge University Press.
  • [4] Dosen, K., Negation in the light of modal logic, in: D.M. Gabbay and H. Wansing eds, What is Negation?, Kluwer, Dordrecht, 1999, pp. 77-86.
  • [5] Dunn, M. J., Positive modal logic, Studia Logica 55 (2), 1995, 301-317.
  • [6] Dzik, W., Orłowska, E., and van Alten,C., Relational representation theorems for lattices with negations: A survey. Lecture Notes in Artificial Intelligence 4342, 2006, 245-266.
  • [7] Esakia, L., The modalized Heyting calculus: a conservative modal extension of the Intuitionistic Logic, Journal of Applied Non-classical Logics 16 (3-4), 2006, 349-366.
  • [8] Fisher Servi, G., On modal logics with an intuitionistic base, Studia Logica 36, 1977, 141-149.
  • [9] Fisher Servi, G., Semantics for a class of intuitionistic modal calculi, Italian Studies in the Philosophy of Science, M. Dalla Chiara (ed), Reidel, 1980, 59-72.
  • [10] Iturrioz, L. and Orłowska, E., A Kripke-style and relational semantics for logics based on Lukasiewicz algebras. Multiple Valued Logic and Soft Computing 12 (1-2), 2006, 131-147.
  • [11] Iturrioz, L., Symmetrical Heyting algebras with Operators, Zeitschrift fuer Mathematische Logik und Grundlagen der Mathematik 29, 1983, 33-70.
  • [12] Jónson, B. and Tarski, A., Boolean algebras with operators, Part I, American Journal of Mathematics 73, 1951, 891-939,
  • [13] Jónson, B. and Tarski, A., Boolean algebras with operators, Part II, American Journal of Mathematics 74, 1952, 127-162.
  • [14] Maksimova L.L., Pretabular superintuitionistic logics, Algebra and Logic 11 (5) (1972), 558-570.
  • [15] Maksimova L.L., Pretabular extensions of the Lewis' logic S4, Algebra and Logic, 14 (1) (1975), 28-55.
  • [16] Orłowska, E., Rewitzky, I. and Düntsch,I., Relational semantics through duality. Lecture Notes in Computer Science 3929, Springer, 2006, 17-32.
  • [17] Orłowska, E. and Rewitzky, I., Duality via Truth: semantic frameworks for lattice-based logics, Logic Journal of the IGPL 13, 2005, 467-490.
  • [18] Palmigiano, A., Dualities for intuitionistic modal logic. Preprint.
  • [19] Priestley, H.A., Representation of distributive lattices by means of ordered Stone spaces, Bulletin of the London Mathematical Society 2, 1970, 186-190.
  • [20] Priestley, H. A., Ordered topological spaces and the representation of distributive lattices, Proceedings of the London Mathematical Society 24, 1972, 507-530.
  • [21] Rauszer, C., Semi-Boolean algebras and their applications to intuitionistic logic with dual operations. Fundamentas Mathematicae 83, 1974, 219-249.
  • [22] Sofronie-Stokkermans,V., Priestley duality for SHn-algebras and applications to the study of Kripke-style models for SHn-logics. Multiple-Valued Logics, an International Journal 5 (4), 2000, 281-305.
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  • [24] Stone, M., The theory of representations of Boolean algebras, Transactions of the American Mathematical Society 40, 1936, 37-111.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS5-0014-0041
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