Algebraic Characterization of the Local Craig Interpolation Property

Authors

  • Zalán Gyenis Department of Logic, Jagiellonian University, Kraków Department of Logic, Eötvös University, Budapest

DOI:

https://doi.org/10.18778/0138-0680.47.1.04

Keywords:

Craig interpolation, Algebraic logic, Superamalgamation

Abstract

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. 

References

[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.
Google Scholar

[2] H. Andréka, I. Németi, I. Sain, Universal Algebraic Logic, Studies in Logic, Springer, due to 2017.
Google Scholar

[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.
Google Scholar

[4] W. J. Blok, D. Pigozzi, Algebraizable logics, Memoirs of the American Mathematical Society, Vol. 77, No. 396, pp. vi+78, 1989.
Google Scholar

[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.
Google Scholar

[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.
Google Scholar

[7] J. Czelakowski, Logical matrices and the amalgamation property, Studia Logica XLI(4) (1982), pp. 329–342.
Google Scholar

[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.
Google Scholar

[9] J. Czelakowski, D. Pigozzi. Fregean logics, Annals of Pure and Applied Logic 127(1/3) (2004), pp. 17–76.
Google Scholar

[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.
Google Scholar

[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.
Google Scholar

[12] Z. Gyenis, Interpolation property and homogeneous structures, Logic Journal of IGPL 22(4) (2014), pp. 597–607.
Google Scholar

[13] L. Henkin, J. D. Monk, A. Tarski, Cylindric Algebras Parts I, II, North Holland, Amsterdam, 1971.
Google Scholar

[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.
Google Scholar

[15] L. L. Maksimova, Amalgamation and interpolation in normal modal logics, Studia Logica L(3/4) (1991), pp. 457–471.
Google Scholar

[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.
Google Scholar

[17] D. Nyíri, Robinson’s property and amalgamations of higher arities, Mathematical Logic Quarterly, Vol. 62, Issue 4–5 (2016), pp. 427–433.
Google Scholar

[18] D. Pigozzi, Amalgamation, Congruence Extension and Interpolation Properties in Algebras, Algebra Universalis 1(3) (1972), pp. 269–349.
Google Scholar

[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.
Google Scholar

[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.
Google Scholar

[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.
Google Scholar

Downloads

Published

2018-03-30

How to Cite

Gyenis, Z. (2018). Algebraic Characterization of the Local Craig Interpolation Property. Bulletin of the Section of Logic, 47(1), 45–58. https://doi.org/10.18778/0138-0680.47.1.04

Issue

Section

Research Article