Scope dominance with upward monotone quantifiers


Abstract
We give a complete characterization of the class of upward monotone generalized quantifiers Q1 and Q2 over countable domains that satisfy the scheme Q1 x Q2 y φ → Q2 y Q1 x 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
Keywords generalized quantifier  monotonicity  scope  dominance
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DOI 10.1007/s10849-005-4960-6
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References found in this work BETA

Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Generalized Quantifiers and Natural Language.Jon Barwise - 1980 - Linguistics and Philosophy 4:159.
Generalized Quantifiers in Linguistics and Logic.D. Keenan & D. Westerstahl - 2011 - In Johan Van Benthem & Alice Ter Meulen (eds.), Handbook of Logic and Language. Elsevier. pp. 837--893.
Scopeless Quantifiers and Operators.Thomas Ede Zimmermann - 1993 - Journal of Philosophical Logic 22 (5):545 - 561.

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Citations of this work BETA

Scope Dominance with Monotone Quantifiers Over Finite Domains.Gilad Ben-Avi & Yoad Winter - 2004 - Journal of Logic, Language and Information 13 (4):385-402.

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