|Abstract||This article studies the monotonicity behavior of plural determiners that quantify over collections. Following previous work, we describe the collective interpretation of determiners such as all, some and most using generalized quantiﬁers of a higher type that are obtained systematically by applying a type shifting operator to the standard meanings of determiners in Generalized Quantiﬁer Theory. Two processes of counting and existential quantiﬁ- cation that appear with plural quantiﬁers are uniﬁed into a single determiner ﬁtting operator, which, unlike previous proposals, both captures existential quantiﬁcation with plural determiners and respects their monotonicity properties. However, some previously unnoticed facts indicate that monotonicity of plural determiners is not always preserved when they apply to collective predicates. We show that the proposed operator describes this behavior correctly, and characterize the monotonicity of the collective determiners it derives. It is proved that determiner ﬁtting always preserves monotonicity properties of determiners in their second argument, but monotonicity in the ﬁrst argument of a determiner is preserved if and only if it is monotonic in the same direction in the second argument. We argue that this asymmetry follows from the conservativity of generalized quantiﬁers in natural language.|
|Keywords||No keywords specified (fix it)|
|Through your library||Only published papers are available at libraries|
Similar books and articles
R. Zuber (2010). A Note on the Monotonicity of Reducible Quantifiers. Journal of Logic, Language and Information 19 (1).
Manfred J. Holler, Rie Ono & Frank Steffen (2001). Constrained Monotonicity and the Measurement of Power. Theory and Decision 50 (4):383-395.
Hans Smessaert (1996). Monotonicity Properties of Comparative Determiners. Linguistics and Philosophy 19 (3):295 - 336.
Juha Kontinen & Jakub Szymanik (2008). A Remark on Collective Quantification. Journal of Logic, Language and Information 17 (2):131-140.
Jouko Väänänen & Dag Westerståhl (2002). On the Expressive Power of Monotone Natural Language Quantifiers Over Finite Models. Journal of Philosophical Logic 31 (4):327-358.
John Nerbonne (1995). Nominal Comparatives and Generalized Quantifiers. Journal of Logic, Language and Information 4 (4):273-300.
Makoto Kanazawa (1994). Weak Vs. Strong Readings of Donkey Sentences and Monotonicity Inference in a Dynamic Setting. Linguistics and Philosophy 17 (2):109 - 158.
Gilad Ben-Avi & Yoad Winter (2003). Monotonicity and Collective Quantification. Journal of Logic, Language and Information 12 (2):127-151.
Added to index2009-01-28
Total downloads5 ( #160,518 of 549,715 )
Recent downloads (6 months)0
How can I increase my downloads?