One Connection between Standard Invariance Conditions on Modal Formulas and Generalized Quantifiers
- Dorit Ben Shalom
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The language of standard propositional modal logic has one operator (□ or ♦), that can be thought of as being determined by the quantifiers ∀ or ∃, respectively: for example, a formula of the form □Φ is true at a point s just in case all the immediate successors of s verify Φ.This paper uses a propositional modal language with one operator determined by a generalized quantifier to discuss a simple connection between standard invariance conditions on modal formulas and generalized quantifiers: the combined generalized quantifier conditions of conservativity and extension correspond to the modal condition of invariance under generated submodels, and the modal condition of invariance under bisimulations corresponds to the generalized quantifier being a Boolean combination of ∀ and ∃.
Goldblatt, R., 1992, Logics of Time and Computation, Stanford, CA: CSLI Publications.
Keenan, E.L. and Westerståhl, D., 1997, “Generalized quantifiers in linguistics and logic,” pp. 837–893 in Handbook of Logic and Language, J. van Benthem and A. ter Meulen, eds, Amsterdam: Elsevier.
van Benthem, J., 1986, Essays in Logical Semantics, Dordrecht: Reidel.
van der Hoek, W., 1992, “Modalities for reasoning about knowledge and quantities,” Dissertation, Free University of Amsterdam.
Westerståhl, D., 1989, “Quantifiers in formal and natural languages,” pp. 1–131 in Handbook of Philosophical Logic, D.M. Gabbay and F. Guenthner, eds, Dordrecht: Reidel.
- One Connection between Standard Invariance Conditions on Modal Formulas and Generalized Quantifiers
Journal of Logic, Language and Information
Volume 12, Issue 1 , pp 47-52
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- generalized quantifiers
- modal logic
- Dorit Ben Shalom (1)
- Author Affiliations
- 1. Department of Foreign Literatures and Linguistics, Ben Gurion University of the Negev, P.O. Box 653, 84105, Beer-Sheva, Israel