On the Expressive Power of Monotone Natural Language Quantiers over Finite Models
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Abstract:
We study denability in terms of monotone generalized quantiers satisfying Isomorphism closure, Conservativity and Extension. Among the quantiers with the latter three properties | here called CE quanti ers | one nds 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 denable in terms of monotone CE quantiers: we give a necessary and sucient condition for such de-nability. We further identify a stronger form of monotonicity, called smoothness, which also has linguistic relevance, and we extend our considerations to smooth quantiers. The results lead us to propose two tentative universals concerning monotonicity and natural language quanti cation. The notions involved as well as our proofs are presented using a graphical representation of quantiers in the so-called number tree.
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