Abstract
We characterize pairs of monotone generalized quantifiers Q 1 and Q 2 over finite domains that give rise to an entailment relation between their two relative scope construals. This relation between quantifiers, which is referred to as scope dominance, is used for identifying entailment relations between the two scopal interpretations of simple sentences of the form NP1–V–NP2. Simple numerical or set-theoretical considerations that follow from our main result are used for characterizing such relations. The variety of examples in which they hold are shown to go far beyond the familiar existential-universal type.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Altman, A. and Winter, Y., 2003, “Computing dominant readings with upward monotone quantifiers,” To appear in Research on Language and Computation, Downloadable at http://www.cs.technion.ac.il/~winter/
Altman, A., Peterzil, Y., and Winter, Y., 2002, “Scope dominance with upward monotone quantifiers,” Unpublished manuscript, Technion and Haifa University, Downloadable at http://www.cs.technion.ac.il/~winter/
Eijck, D. J. N. and Jaspars, J. O. M., 1996, “Ambiguity and Reasoning,” Technical report, Computer Science/Department of Software Technology, Centrum voor Wiskunde en Informatica (CWI), CS-R9616.
Reyle, U., 1993, “Dealing with ambiguities by underspecification: Construction, representation, and deduction,” Journal of Semantics 10, 123–179.
Reyle, U., 1995, “On reasoning with ambiguities,” in Proceedings of the EACL’95.
Reyle, U., 1996, “Co-indexing labelled DRSS to represent and reason with ambiguities,” in Semantic Ambiguity and Underspecification, K. van Deemter and S. Peters, eds. Stanford: CSLI Publications.
Vänänen, J. and Westerståhl, D., 2002, “On the expressive power of monotone natural language quantifiers over finite sets,” Journal of Philosophical Logic 31, 327–358.
van Benthem, J., 1989, “Polyadic quantifiers,” Linguistics and Philosophy 12, 437–464.
van Deemter, K., 1998, “Ambiguity and Idiosyncratic Interpretation,” Journal of Semantics 15, 5–36.
van Deemter, K., 1996, “Towards a Logic of Ambiguous Expressions,” in Semantic Ambiguity and Underspecification, K. van Deemter and S. Peters, eds. Cambridge, U.K.: Cambridge University Press, Sweden, pp. 203–237.
Westerståhl, D., 1986, “On the order between quantifiers,” in Acta Universitatis Gothoburgensis, M. Furberg, eds., Göteborg University, pp. 273–285.
Westerståhl, D., 1996, “Self-commuting quantifiers,” The Journal of Symbolic Logic 61, 212–224.
Zimmermann, T. E., 1993, “Scopeless quantifiers and operators,” Journal of Philosophical Logic 22, 545–561.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ben-Avi, G., Winter, Y. Scope Dominance with Monotone Quantifiers over Finite Domains. J Logic Lang Inf 13, 385–402 (2004). https://doi.org/10.1007/s10849-004-2112-z
Issue Date:
DOI: https://doi.org/10.1007/s10849-004-2112-z