Abstract
Interpolation and definability play an important part in the mathematical logic. We consider different versions of these properties. Let L be any propositional logic.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beth, W.E.: 1953, “On Padoa’s method in the theory of definitions”, Indag. Math. Vol.15, no.4, pp. 330–339
Czelakowski, J.: 1982, “Logical matrices and the amalgamation property”, Studia Logica Vol.41, no.4, pp. 329–341
Gabbay, D.M.: 1972, “Craig’s interpolation theorem for modal logic”. Conference in Math. Logic, London’70, Berlin, Springer, pp. 111–127
Gurevich, Y.: 1984, “Toward logic tailored for computational complexity”, Computation and proof theory. Lecture Notes in Math., 1104, Berlin, Springer, pp. 175–216
Henkin, L., Monk, J.D., and Tarski, A.: 1985, Cylindric Algebras, Part II. North-Holland, Amsterdam
Kawai, H.: 1982, “Eine Logic Erster Stufe mit einem infinitaren Zeitoperator”, Zeitschrift für mathematischer Logik und Grundlagen Mathematik 28, pp. 173–180
Kroeger, F.: 1987, “Temporal logics of programs”, EATS Monograph on Theoretical Computer Science, Berlin, Springer
Maksimova, L.L.: 1979, “Interpolation theorems in modal logics and amalgamated varieties of topoboolean algebras”, (in Russian). Algebra i Logika 18, no.5, pp. 556–586
Maksimova, L.L.: 1982, “Failure of the interpolation property in modal counterparts of Dummett’s logic”, (in Russian). Algebra i Logika 21, no.6 pp. 690–694
Maksimova, L.L.: 1989a, “Interpolation in modal logics of infinite slice containing K4”, (in Russian). Matematiceskaya logika i algoritmiceskie problemy, Novosibirsk, Nauka (Sib. Div.), pp. 73–91
Maksimova, L.L.: 1989b, “Definability theorems in normal extensions of the provability logic”, Studia Logica 48, no.4, pp. 495–507
Maksimova, L.L.: 1989c, “Interpolation, the Beth property and the tense logic of ‘tomorrow’” Preprint, Institute of Mathematics, Sib. Div. of Acad. Sei. of USSR, Novosibirsk
Maksimova, L.L.: 1990, “Temporal logics with discrete moments of time and the Beth property”, in: Proceedings of the 4th Asian Logical Conference, Sept. 1990, Tokyo, Japan, pp. 31–34
Manna, Z. and Pnueli, A.: 1983, “Verification of concurrent programs: a temporal proof system”, in: Foundations of Computer Science TV (Math. Centre tracts), Amsterdam, pp. 163–255
Manna, Z. and Wolper, P.: 1982, “Synthesis of communicating processes from temporal logic specifications”, in: Logic of Programs Proceedings Conference New York’81, D. Kozen (ed.), Springer LNCS, 131, pp. 253–281
Nemeti, I.: 1982, “Nonstandard Dynamic Logic”, in: Logic of Programs. Proceedings Conference New York’81, D. Kozen (ed.), Springer LNCS, 131, 1982, pp. 311–348
Smorynski, C.:1978, “Beth’s theorem and self-referential sentences”, In: Logic Colloquium’77, North-Holland, Amsterdam, pp. 253–261
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Maksimova, L. (1995). Implicit and Explicit Definability in Modal and Temporal Logics. In: Pólos, L., Masuch, M. (eds) Applied Logic: How, What and Why. Synthese Library, vol 247. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8533-0_6
Download citation
DOI: https://doi.org/10.1007/978-94-015-8533-0_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4536-2
Online ISBN: 978-94-015-8533-0
eBook Packages: Springer Book Archive