Scope Dominance with Upward Monotone Quantifiers
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We give a complete characterization of the class of upward monotone generalized quantifiers Q1 and Q2 over countable domains that satisfy the scheme Q1xQ2y φ → Q2yQ1x φ. 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 infinite domains, there are more general types of quantifiers that support these entailments.
Keywordsgeneralized quantifier monotonicity scope dominance
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