Abstract
In the seventies it was discovered that sometimes modal propositional formulas have a rather big expressive power: there are modal formulas without first-order equivalents on Kripke frames,1 see [4]. The main typical means for obtaining such results are the Löwenheim-Skolem theorem and the compactness theorem. However, by the Lindström theorem (Theorem 2.5.4 [9]) these effects are very strong: both theorems together characterize first-order logic completely. It is natural to raise the question: what specific properties of first-order formulas are true for modal formulas (on interesting classes of frames).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bellissima, F., ‘An Effective Representation for Finitely Generated Free Interior Algebras’, Algebra Universalis, 20 (1985), 302–317.
Bellissima, E, ‘Post Complete and 0-Axiomatizablc Modal Logics’, Ann. Pure Appl. Logic, 47 (1990), 121–144.
Van Benthem, J. E A. K., ‘Canonical Modal Logics and Ultrafilter Extensions’,. 1. Symbolic Logic, 44 (1979), 25–37.
Van Benthem, J. F. A. K., Modal Logic and Classical Logic, Bibliopolis, Naples, 1986.
Van Benthem, J. F. A. K., ‘Notes on Modal Definability’, Notre Dame J. Formal Logic, 39 (1989), 20–39.
Blok, W. J., ‘Pretabular Varieties of Modal Algebras’, Studio Logica, 39 (2/3) (1980), 101–124.
Chagrov, A. V., Nontabularity — Pretabularity, Antitabularity, Coantitabularity’, in Algebraic and Logical Constructions, Kalinin State University, Kalinin, 1989, pp. 105–111.
Chagrov, A. V. and Zakharyaschev, M. V., Modal Logic, Oxford University Press, 1997.
Chang, C. C. and Jerome Keisler, H., Model Theory, 3rd edn, Elsevier Science Publishers, 1990.
Goldblatt, R. I., ‘Metamathematics of Modal Logic’, Reports on Mathematical Logic, 6 (1976), 4177; 7, 21–52.
Maksimova, L. L., Pretabular Extensions of Lewis S4, Algebra and Logic, 14 (1975), 16–33.
Maksimova, L. L., ‘Modal Logics of Finite Slices’, Algebra and Logic, 14 (1975), 188–197.
Maksimova, L. L., ‘Interpolation in the Modal Logics of the Infinite Slice Containing K4’, in Mathematical Logic and Algorithmic Problems, Nauka, Novosibirsk, 1989, pp. 73–91.
Rybakov, V. V., ‘Criateria for Admissibility of Inference Rules, Modal and Intermediate Logics with the Branching Property’, Stadia Logica, 53 (1994), 203–226.
Segerberg, K., An Essay in Classical Modal Logic, Filosofiska Studier, Uppsala, 1971, p. 13.
Shehtman, V. B., ‘Rieger-Nishimura Lattices’, Soviet Math. Dokl., 19 (1978), 1014–1018.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Chagrov, A.V. (1999). A First-Order Effect and Modal Propositional Formulas. In: Cantini, A., Casari, E., Minari, P. (eds) Logic and Foundations of Mathematics. Synthese Library, vol 280. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2109-7_15
Download citation
DOI: https://doi.org/10.1007/978-94-017-2109-7_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5201-8
Online ISBN: 978-94-017-2109-7
eBook Packages: Springer Book Archive