Referential semantics: duality and applications

• Autorzy: Jansana R. , Palmigiano A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, Wojcicki's characterization of selfex- tensional logics as those logics that are endowed with a complete local referential semantics is extended to a fully edged duality between atlas-models (i.e. generalized matrix models) and refer- ential models of an arbitrary selfextensional logic S. This duality serves as a general template where a wide range of Stone- and Priestley-style dualities related with concrete logics can t. The rst application of this duality is a characterization of the fully selfextensional logics among the selfextensional ones. Fully selfex- tensional logics form a subclass of particularly well-behaved selfex- tensional logics, and only recently [1] this inclusion was shown to be proper. In this paper, fully selfextensional logics are character- ized as those selfextensional logics S whose algebraic counterpart Alg(S) { seen as a category { is dually equivalent to the reduced referential models of S. This implies that if S is fully selfexten- sional, then every algebra in Alg(S) is isomorphic to an algebra of sets.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2006
• Tom: Nr 41,spec. iss.
• Strony: 63--93
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Jansana R.

autor

Palmigiano A.

• Departament de Logica, Historia i Filosoa de la Ciencia Universitat de Barcelona Baldiri i Reixach s/n 08028 Barcelona, Spain,

Bibliografia

• [1] S.V. Babyonishev, Fully Fregean logics, Reports on Mathematical Logic 37 (2003), pp. 59-78.
• [2] N. Belnap, A useful four-valued logic, in: Modern uses of Multiple-Valued Logic, J.M. Dunn, G. Epstein, Eds. Reidel, Dordrecht-Boston, 1977, pp. 8-37.
• [3] D.J. Brown and R. Suszko, Abstract Logics, Disertationes mathematicae bf 102 (1973), pp. 9-42.
• [4] S. Celani and R. Jansana, A closer look at some subintuitionistic logics, Notre Dame Journal of Formal Logic 42 (2001), printed (2003), pp. 225-255.
• [5] S. Celani and R. Jansana, A new semantics for positive modal logic, Notre Dame Journal of Formal Logic 38 (1997), pp. 1-18.
• [6] J. Czelakowski, Protoalgebraic Logics, Kluwer, Dordrecht 2001.
• [7] M. Dunn and G.M. Hardegree, Algebraic Methods in Philosophical Logic, Oxford University Press, Oxford 2001.
• [8] J.M. Font Belnap's Four-Valued Logic and De Morgan Lattices, Logic Journal of the I.G.P.L- 5 (1997), pp. 413-440.
• [9] J.M. Font and R. Jansana, A General Algebraic Semantics for Sentential Logics, Springer, Berlin 1996.
• [10] J.M. Font, R. Jansana, and D. Pigozzi, A Survey on Abstract Algebraic Logic, Studia Logica 74 (2003), pp. 13-97.
• [11] J.M. Font and V. Verdú, Algebraic Logic for Classical Conjunction and Disjunction, Studia Logica 50 (1991), pp. 391-419.
• [12] R. Jansana, Full Models for Positive Modal Logic, Mathematical Logic Quarterly 48 (2002), pp. 427-445.
• [13] R. Jansana, Selfextensional logics with conjunction, Preprint 2004.
• [14] A. Visser, A propositional logic with explicit fixed points, Studia Logica 40 (1981), pp. 155-75.
• [15] R. Wójcicki, Logical matrices strongly adequate for structural sentential calculi, Bulletin of l'Acadmie Polonaise des Sciences, Serie des sciences mathematiques et phisiques 6 (1969), pp. 333-335.
• [16] R. Wójcicki, Referential Matrix Semantics for Propositional Calculi, in: Proceedings of the Sixth International Congress of Logic, Methodology and Philosophy of Science, Hannover 1979, North-Holland and PWN (1982), pp. 325-334.
• [17] R. Wójcicki, Theory of Logical Calculi. Basic Theory of Consequence Operations, Kluwer, Dordrecht 1988.