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Categorical Abstract Algebraic Logic: Full Models, Frege Systems and Metalogical Properties

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Abstrakty
EN
Font and Jansana studied the full models of sentential logics under the presence of a variety of metalogical properties. Their theory of full models was adapted, in recent work by the author, to cover the case of institutional logics. In the present work, the study of metalogical properties is carried out in the -institution framework and the way they aect full models of -institutions is investigated.
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31--60
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
  • School of Mathematics and Computer Science Lake Superior State University Sault Sainte Marie, MI 49783, USA, gvoutsad@lssu.edu
Bibliografia
  • [1] S.V. Babyonyshev, Fully Fregean Logics, Reports on Mathematical Logic 37 (2003), pp. 59-78.
  • [2] M. Barr, and C. Wells, Category Theory for Computing Science, Third Edition, Les Publications CRM, Montréal 1999.
  • [3] W.J. Blok, and D. Pigozzi, Algebraizable Logics, Memoirs of the American Mathematical Society, Vol. 77, No. 396 (1989)
  • [4] W.J. Blok and D. Pigozzi, Algebraic Semantics for Universal Horn Logic Without Equality, in Universal Algebra and Quasigroup Theory, A. Romanowska and J.D.H. Smith, Eds., Heldermann Verlag, Berlin 1992.
  • [5] W.J. Blok and D. Pigozzi, Abstract Algebraic Logic and the Deduction Theorem, to appear in the Bulletin of Symbolic Logic.
  • [6] F. Borceux, Handbook of Categorical Algebra, Encyclopedia of Mathematics and its Applications, Vol. 50, Cambridge University Press, Cambridge, U.K., 1994.
  • [7] J. Czelakowski, Logical Matrices and the Amalgamation Property, Studia Logica 41, 4 (1982), pp. 329-341.
  • [8] J. Czelakowski, Sentential Logics and Maehara Interpolation Property, Studia Logica 44, 3 (1985), pp. 265-283.
  • [9] J. Czelakowski, Local Deduction Theorems, Studia Logica 45, 4 (1986), pp. 377-391
  • [10] J. Czelakowski, Protoalgebraic Logics, Studia Logica Library 10, Kluwer, Dordrecht 2001.
  • [11] J. Czelakowski and D. Pigozzi, Fregean Logics, Annals of Pure and Applied Logic 127 (2004), pp. 17-76
  • [12] J. Czelakowski, and D. Pigozzi, Fregean logics with the multiterm deduction theorem and their algebraization, Studia Logica 78, 1-2 (2004), pp. 171-212.
  • [13] J. Fiadeiro and A. Sernadas, Structuring Theories on Consequence, in: Recent Trends in Data Type Specification, Donald Sannella and Andrzej Tarlecki, Eds., Lecture Notes in Computer Science, Vol. 332, Springer-Verlag, New York 1988, pp. 44-72.
  • [14] J.M. Font and R. Jansana, A General Algebraic Semantics for Sentential Logics, Lecture Notes in Logic, Vol. 7 (1996), Springer-Verlag, Berlin - Heidelberg 1996.
  • [15] Font, J.M., Jansana, R., and Pigozzi, D., A Survey of Abstract Algebraic Logic, Studia Logica 74, 1/2 (2003), pp. 13-97
  • [16] J.A. Goguen and R.M. Burstall, 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.
  • [17] J.A. Goguen and R.M. Burstall, Institutions: Abstract Model Theory for Specification and Programming, Journal of the Association for Computing Machinery 39, 1 (1992), pp. 95-146.
  • [18] S. Mac Lane, Categories for the Working Mathematician, Springer-Verlag, 1971.
  • [19] A. Tarlecki, Bits and Pieces of the Theory of Institutions, Category Theory and Computer Programming (Guildford, 1985), Lecture Notes in Computer Science, Vol. 240 (1986), pp. 334-363.
  • [20] G. Voutsadakis, Categorical Abstract Algebraic Logic, Doctoral Dissertation, Iowa State University, Ames, Iowa 1998.
  • [21] G. Voutsadakis, Categorical Abstract Algebraic Logic: Equivalent Institutions, Studia Logica 74, 1/2 (2003), pp. 275-311.
  • [22] G. Voutsadakis, Categorical Abstract Algebraic Logic: Algebraizable Institutions, Applied Categorical Structures 10, 6 (2002), pp. 531-568
  • [23] G. Voutsadakis, Categorical Abstract Algebraic Logic: Metalogical Properties, Studia Logica 74 (2003), pp. 369-398
  • [24] G. Voutsadakis, 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://pigozzi.lssu.edu/WWW/research/papers.html
  • [25] G. Voutsadakis, Categorical Abstract Algebraic Logic: Models of pi-Institutions, Notre Dame Journal of Formal Logic 46 (4) (2005), pp. 439-460.
  • [26] G. Voutsadakis, Categorical Abstract Algebraic Logic: Generalized Tarski Congruence Systems, Submitted to Theory and Applications of Categories, Preprint available at http://pigozzi.lssu.edu/WWW/research/papers.html
  • [27] G. Voutsadakis, Categorical Abstract Algebraic Logic: (I;N)-Algebraic Systems, Applied Categorical Structures 13 (3) (2005), pp. 265-280.
  • [28] G. Voutsadakis, Categorical Abstract Algebraic Logic: Gentzen pi-Institutions, Submitted to Mathematica Scandinavica, Preprint available at http://pigozzi.lssu.edu/WWW/research/papers.html
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ6-0021-0009
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