Categorical Abstract Algebraic Logic: Strong Version of a Protoalgebraic pi-Institution

• Autorzy: Voutsadakis G.
• Języki publikacji: EN

Abstrakty

EN

An analog of the strong version of a protoalge- braic logic, introduced by Font and Jansana, is presented for N- protoalgebraic -institutions. Some properties of this strong ver- sion of an N-protoalgebraic -institution are explored and they are related to the explicit denability of N-Leibniz theory sys- tems. N-Leibniz theory systems were introduced in previous work by the author, also taking after the corresponding theory of Font and Jansana in the sentential framework.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2007
• Tom: No. 42
• Strony: 19--46
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Voutsadakis G.

• School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, USA,

Bibliografia

• [1] Barr, M., and Wells, C., Category Theory for Computing Science, Third Edition, Les Publications CRM, Montreal 1999.
• [2] Blok, W.J., and Pigozzi, D., Protoalgebraic Logics, Studia Logica, Vol. 45 (1986), pp. 337-369
• [3] Blok, W.J., and Pigozzi, D., Algebraizable Logics, Memoirs of the American Mathematical Society, Vol. 77, No. 396 (1989)
• [4] Borceux, F., Handbook of Categorical Algebra, Encyclopedia of Mathematics and its Applications, Vol. 50, Cambridge University Press, Cambridge, U.K., 1994.
• [5] Czelakowski, J., Equivalential Logics I,II, Studia Logica, Vol. 40 (1981), pp. 227-236, 355-372
• [6] Czelakowski, J., Protoalgebraic Logics, Studia Logica Library 10, Kluwer, Dordrecht, 2001
• [7] Czelakowski, J., and Jansana, R., Weakly Algebraizable Logics, Journal of Symbolic Logic, Vol. 65, No. 2 (2000), pp. 641-668
• [8] Fiadeiro, J., and Sernadas, A., Structuring Theories on Consequence, in Recent Trends in Data Type Specification, Donald Sannella and Andrzei Tarlecki, Eds.,Lecture Notes in Computer Science, Vol. 332, Springer-Verlag, New York 1988, pp. 44-72
• [9] Font, J.M., and Jansana, R., A General Algebraic Semantics for Sentential Logics, Lecture Notes in Logic, Vol. 7 (1996), Springer-Verlag, Berlin Heidelberg 1996
• [10] Font, J.M., and Jansana, R., Leibniz Filters and the Strong Version of a Protoalgebraic Logic, Archive for Mathematical Logic, Vol. 40 (2001), pp. 437-465
• [11] Font, J.M., Jansana, R., and Pigozzi, D., A Survey of Abstract Algebraic Logic, Studia Logica, Vol. 74, No. 1/2 (2003), pp. 13-97
• [12] Goguen, J.A., and Burstall, R.M., Introducing Institutions, in Proceedings of the Logic of Programming Workshop, E. Clarke and D. Kozen, Eds., Lecture Notes in Computer Science, Vol. 164, Springer-Verlag, New York 1984, pp. 221-256
• [13] Goguen, J.A., and Burstall, R.M., Institutions: Abstract Model Theory for Specification and Programming, Journal of the Association for Computing Machinery, Vol.39, No. 1 (1992), pp. 95-146
• [14] Jansana, R., Leibniz Filters Revisited, Studia Logica, Vol. 75 (2003), pp. 305-317
• [15] Mac Lane, S., Categories for the Working Mathematician, Springer-Verlag, 1971.
• [16] Voutsadakis, G., Categorical Abstract Algebraic Logic: Tarski Congruence Systems, Logical Morphisms and Logical Quotients, Submitted to the Annals of Pure and Applied Logic, Preprint available at http://www.voutsadakis.com/RESEARCH/papers.html
• [17] Voutsadakis, G., Categorical Abstract Algebraic Logic: Models of pi-Institutions, Notre Dame Journal of Formal Logic, Vol. 46, No. 4 (2005), pp. 439-460
• [18] Voutsadakis, G., Categorical Abstract Algebraic Logic: Generalized Tarski Congruence Systems, Submitted to Theory and Applications of Categories, Preprint available at http://www.voutsadakis.com/RESEARCH/papers.html
• [19] Voutsadakis, G., Categorical Abstract Algebraic Logic: (I;N)-Algebraic Systems, Applied Categorical Structures, Vol. 13, No. 3 (2005), pp. 265-280
• [20] Voutsadakis, G., Categorical Abstract Algebraic Logic: Gentzen pi-Institutions, Preprint available at http://www.voutsadakis.com/RESEARCH/papers.html
• [21] Voutsadakis, G., Categorical Abstract Algebraic Logic: Full Models, Frege Systems and Metalogical properties, Reports on Mathematical Logic, Vol. 41 (2006), pp. 31-62
• [22] Voutsadakis, G., Categorical Abstract Algebraic Logic: Prealgebraicity and Protoalgebraicity, To appear in Studia Logica, Preprint available at http://www.voutsadakis.com/RESEARCH/papers.html
• [23] Voutsadakis, G., Categorical Abstract Algebraic Logic: More on Protoalgebraicity, To appear in the Notre Dame Journal of Formal Logic, Preprint available at http://www.voutsadakis.com/RESEARCH/papers.html
• [24] Voutsadakis, G., Categorical Abstract Algebraic Logic: Protoalgebraicity and Leibniz Theory Systems, Scientiae Mathematicae Japonicae, Vol. 62, No. 1 (2005), pp. 109-117
• [25] Voutsadakis, G., Categorical Abstract Algebraic Logic: The Largest Theory System Included in a Theory Family, Mathematical Logic Quarterly, Vol. 52, No. 3 (2006), pp. 288-294
• [26] Voutsadakis, G., Categorical Abstract Algebraic Logic: Weakly Algebraizable pi-Institutions, Submitted to Studia Logica, Preprint available at http://www.voutsadakis.com/RESEARCH/papers.html
• [27] Voutsadakis, G., Categorical Abstract Algebraic Logic: Equivalential pi-Institutions, To appear in the Australasian Journal of Logic, Preprint available at http://www.voutsadakis.com/RESEARCH/papers.html