Scope dominance with upward monotone quantifiers

Alon Altman; Ya'acov Peterzil; Yoad Winter

doi:10.1007/s10849-005-4960-6

Scope dominance with upward monotone quantifiers

Alon Altman, Ya'acov Peterzil, Yoad Winter

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We give a complete characterization of the class of upward monotone generalized quantifiers Q ₁ and Q ₂ over countable domains that satisfy the scheme Q ₁ x Q ₂ y φ → Q ₂ y Q ₁ x φ. This generalizes the characterization of such quantifiers over finite domains, according to which the scheme holds iff Q ₁ is ∃ or Q ₂ is ∀ (excluding trivial cases). Our result shows that in infinite domains, there are more general types of quantifiers that support these entailments.

Original language	English
Pages (from-to)	445-455
Number of pages	11
Journal	Journal of Logic, Language and Information
Volume	14
Issue number	4
DOIs	https://doi.org/10.1007/s10849-005-4960-6
State	Published - Oct 2005

Bibliographical note

Funding Information:
The first and third authors were partly supported by grant no. 1999210 (“Extensions and Implementations of Natural Logic”) from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. The third author is grateful for the UiL OTS of Utrecht University, where part of this research was conducted. We are indebted to two anonymous JLLI referees for their useful remarks on a previous draft.

Keywords

Dominance
Generalized quantifier
Monotonicity
Scope

ASJC Scopus subject areas

Computer Science (miscellaneous)
Philosophy
Linguistics and Language

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10.1007/s10849-005-4960-6

Cite this

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AU - Peterzil, Ya'acov

AU - Winter, Yoad

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N2 - We give a complete characterization of the class of upward monotone generalized quantifiers Q 1 and Q 2 over countable domains that satisfy the scheme Q 1 x Q 2 y φ → Q 2 y Q 1 x φ. This generalizes the characterization of such quantifiers over finite domains, according to which the scheme holds iff Q 1 is ∃ or Q 2 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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Scope dominance with upward monotone quantifiers

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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