Journal of Philosophical Logic 31 (4):327-358 (2002)

Authors
Jouko A Vaananen
University of Helsinki
Abstract
We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties - here called CE quantifiers - one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further identify a stronger form of monotonicity, called smoothness, which also has linguistic relevance, and we extend our considerations to smooth quantifiers. The results lead us to propose two tentative universals concerning monotonicity and natural language quantification. The notions involved as well as our proofs are presented using a graphical representation of quantifiers in the so-called number triangle
Keywords definability   generalized   monotonicity   quantifiers
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1019934611163
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,172
Through your library

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.
Essays in Logical Semantics.Johan van Benthem - 1988 - Studia Logica 47 (2):172-173.

View all 15 references / Add more references

Citations of this work BETA

Generalized Quantifiers.Dag Westerståhl - 2008 - Stanford Encyclopedia of Philosophy.
Scope Dominance with Monotone Quantifiers Over Finite Domains.Gilad Ben-Avi & Yoad Winter - 2004 - Journal of Logic, Language and Information 13 (4):385-402.

Add more citations

Similar books and articles

Generalized Quantifiers, and Beyond.Hanoch Ben-Yami - 2009 - Logique Et Analyse (208):309-326.
Definability of Polyadic Lifts of Generalized Quantifiers.Lauri Hella, Jouko Väänänen & Dag Westerståhl - 1997 - Journal of Logic, Language and Information 6 (3):305-335.
Scope Dominance with Upward Monotone Quantifiers.Alon Altman, Ya'Acov Peterzil & Yoad Winter - 2005 - Journal of Logic, Language and Information 14 (4):445-455.
Scope Dominance with Monotone Quantifiers Over Finite Domains.Gilad Ben-Avi & Yoad Winter - 2004 - Journal of Logic, Language and Information 13 (4):385-402.
Unary Quantifiers on Finite Models.Jouko Väänänen - 1997 - Journal of Logic, Language and Information 6 (3):275-304.

Analytics

Added to PP index
2009-01-28

Total views
100 ( #118,233 of 2,517,898 )

Recent downloads (6 months)
6 ( #117,058 of 2,517,898 )

How can I increase my downloads?

Downloads

My notes