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.
Bibliographical noteFunding 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.
- Generalized quantifier
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- Linguistics and Language