Abstract
A class of Kripke frames is called modally definable if there is a set of modal formulas such that the class consists exactly of frames on which every formula from that set is valid, i.e. globally true under any valuation. Here, existential definability of Kripke frame classes is defined analogously, by demanding that each formula from a defining set is satisfiable under any valuation. The notion of modal definability is then generalized by combining these two. Model theoretic characterizations of these types of definability are given.
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.
Similar content being viewed by others
References
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press (2001)
Chang, C.C., Keisler, H.J.: Model Theory. Elsevier (1990)
de Rijke, M., Sturm, H.: Global Definability in Basic Modal Logic. In: Wansing, H. (ed.) Essays on Non-classical Logic. World Scientific Publishers (2001)
Goldblatt, R.I., Thomason, S.K.: Axiomatic classes in propositional modal logic. In: Crossley, J. (ed.) Algebra and Logic, pp. 163–173. Springer (1974)
Goranko, V., Passy, S.: Using the Universal Modality: Gains and Questions. Journal of Logic and Computation 2, 5–30 (1992)
Goranko, V., Vakarelov, D.: Sahlqvist Formulas in Hybrid Polyadic Modal Logics. Journal of Logic and Computation 11, 737–754 (2001)
Hollenberg, M.: Characterizations of Negative Definability in Modal Logic. Studia Logica 60, 357–386 (1998)
Perkov, T., Vuković, M.: Some characterization and preservation theorems in modal logic. Annals of Pure and Applied Logic 163, 1928–1939 (2012)
Perkov, T.: Towards a generalization of modal definability. In: Lassiter, D., Slavkovik, M. (eds.) New Directions in Logic, Language, and Computation. LNCS, vol. 7415, pp. 130–139. Springer, Heidelberg (2012)
Sahlqvist, H.: Completeness and correspondence in the first and second order semantics for modal logic. In: Kanger, S. (ed.) Proceedings of the Third Scandinavian Logic Symposium, Uppsala 1973, pp. 110–143. North-Holland, Amsterdam (1975)
van Benthem, J.: The range of modal logic. Journal of Applied Non-Classical Logics 9, 407–442 (1999)
Venema, Y.: Derivation rules as anti-axioms in modal logic. Journal of Symbolic Logic 58, 1003–1034 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Perkov, T. (2014). A Generalization of Modal Frame Definability. In: Colinet, M., Katrenko, S., Rendsvig, R.K. (eds) Pristine Perspectives on Logic, Language, and Computation. ESSLLI ESSLLI 2013 2012. Lecture Notes in Computer Science, vol 8607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44116-9_10
Download citation
DOI: https://doi.org/10.1007/978-3-662-44116-9_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44115-2
Online ISBN: 978-3-662-44116-9
eBook Packages: Computer ScienceComputer Science (R0)