Scope Dominance with Upward Monotone Quantifiers

By Alon Altman, Ya'acov Peterzil & Yoad Winter

We give a complete characterization of the class of upward monotone generalized quantifiers Q₁ and Q₂ over countable domains that satisfy the scheme Q₁xQ₂yφ→Q₂yQ₁xφ.
This generalizes the characterization of such quantifiers over finite domains, according to which the scheme holds iff Q₁ is ∃ or Q₂ is ∀ (excluding trivial cases). Our result shows that in innite domains, there are more general types of quantifiers that support these entailments.

Published in Journal of Logic, Language and Information, Volume 14, Number 4, October 2005, pp. 445-455(11)

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Posted by Tony Marmo at 00:26 GMT

Updated: Saturday, 25 November 2006 19:51 GMT

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