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2018 | 47 | 1 |
Tytuł artykułu

Algebraic Characterization of the Local Craig Interpolation Property

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The sole purpose of this paper is to give an algebraic characterization, in terms of a superamalgamation property, of a local version of Craig interpolation theorem that has been introduced and studied in earlier papers. We continue ongoing research in abstract algebraic logic and use the framework developed by Andréka– Németi and Sain. 
Rocznik
Tom
47
Numer
1
Opis fizyczny
Daty
wydano
2018-03-30
Twórcy
  • Department of Logic, Jagiellonian University, Kraków Department of Logic, Eötvös University, Budapest
Bibliografia
  • [1] H. Andréka, I. Németi, I. Sain, Algebraic Logic, [in:] D. M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic Vol. II, Second edition, Kluwer Academic Publishers, 2001, pp. 133–247.
  • [2] H. Andréka, I. Németi, I. Sain, Universal Algebraic Logic, Studies in Logic, Springer, due to 2017.
  • [3] H. Andréka, Á. Kurucz, I. Németi, I. Sain, Applying algebraic logic; A general methodology, Lecture Notes of the Summer School “Algebraic Logic and the Methodology of Applying it”, Budapest 1994.
  • [4] W. J. Blok, D. Pigozzi, Algebraizable logics, Memoirs of the American Mathematical Society, Vol. 77, No. 396, pp. vi+78, 1989.
  • [5] W. J. Blok, D. Pigozzi, Abstract Algebraic Logic, Lecture Notes of the Summer School “Algebraic Logic and the Methodology of Applying it”, Budapest 1994.
  • [6] W. J. Blok, D. Pigozzi, Local Deduction Theorems in Algebraic Logic, [in:] J. D. Monk, H. Andréka and I. Németi (eds.), Algebraic Logic (Proc. Conf. Budapest 1988), Vol. 54 of Colloq. Math. Soc. János Bolyai, North- Holland, Amsterdam, 1991, pp. 75–109.
  • [7] J. Czelakowski, Logical matrices and the amalgamation property, Studia Logica XLI(4) (1982), pp. 329–342.
  • [8] J. Czelakowski, D. Pigozzi, Amalgamation and Interpolation in abstract algebraic logic, [in:] Models, Algebras, and Proofs, selected papers of the X Latin American symposium on mathematical logic held in Bogotá, Xavier Caicedo and Carlos H. Montenegro (eds.), Lecture Notes in Pure and Applied Mathematics, Vol. 203, Marcel Dekker, Inc., New York, 1999.
  • [9] J. Czelakowski, D. Pigozzi. Fregean logics, Annals of Pure and Applied Logic 127(1/3) (2004), pp. 17–76.
  • [10] J. M. Font, R. Jansana, A comparison of two approaches to the algebraization of logics, Lecture Notes of the Summer School “Algebraic Logic and the Methodology of Applying it”, Budapest 1994.
  • [11] J. M. Font, R. Jansana, On the Sentential Logics Associated with strongly nice and Semi-nice General Logics, Bulletin of the IGPL, Vol. 2, No. 1 (1994), pp. 55–76.
  • [12] Z. Gyenis, Interpolation property and homogeneous structures, Logic Journal of IGPL 22(4) (2014), pp. 597–607.
  • [13] L. Henkin, J. D. Monk, A. Tarski, Cylindric Algebras Parts I, II, North Holland, Amsterdam, 1971.
  • [14] J. Madarász, Interpolation and Amalgamation, Pushing the Limits. Part I and Part II, Studia Logica, Vol. 61 and 62(3 and 1), (1998 and 1999), pp. 311–345 and pp. 1–19.
  • [15] L. L. Maksimova, Amalgamation and interpolation in normal modal logics, Studia Logica L(3/4) (1991), pp. 457–471.
  • [16] L. L. Maksimova, Interpolation theorems in modal logics and amalgamable varieties of topoboolean algebras, (in Russian), Algebra i logika 18, 5 (1979), pp. 556–586.
  • [17] D. Nyíri, Robinson’s property and amalgamations of higher arities, Mathematical Logic Quarterly, Vol. 62, Issue 4–5 (2016), pp. 427–433.
  • [18] D. Pigozzi, Amalgamation, Congruence Extension and Interpolation Properties in Algebras, Algebra Universalis 1(3) (1972), pp. 269–349.
  • [19] D. Pigozzi, Fregean algebraic logic, [in:] J. D. Monk, H. Andréka and I. Németi (eds.), Algebraic Logic (Proc. Conf. Budapest 1988), Vol. 54 of Colloq. Math. Soc. János Bolyai, North–Holland, Amsterdam, 1991, pp. 475–502.
  • [20] I. Sain, Beth’s and Craig’s properties via epimorphisms and amalgamation in algebraic logic, Algebraic Logic and Universal Algebra in Computer Science, Bergman, Maddux and Pigozzi (eds.), Lecture Notes in Computer Science, Vol. 425, Springer-Verlag, Berlin, 1990, pp. 209–226.
  • [21] G. Sági, S. Shelah, On Weak and Strong Interpolation in Algebraic Logics, Journal of Symbolic Logic, Vol. 71, No. 1, (2006), pp. 104–118.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_18778_0138-0680_47_1_04
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