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Scope Dominance with Upward Monotone Quantifiers

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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.

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Authors and Affiliations

  1. Israeli Institute of Technology, Israel

    Alon Altman (Technion) & Yoad Winter (Technion)

  2. University of Haifa, Israel

    Ya'Acov Peterzil

Authors
  1. Alon Altman
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  2. Ya'Acov Peterzil
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  3. Yoad Winter
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Correspondence to Alon Altman.

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Altman, A., Peterzil, Y. & Winter, Y. Scope Dominance with Upward Monotone Quantifiers. J Logic Lang Inf 14, 445–455 (2005). https://doi.org/10.1007/s10849-005-4960-6

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  • DOI: https://doi.org/10.1007/s10849-005-4960-6

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