**Topic:** **HUMAN SEMANTICS**

### Domains of Measurement: Formal Properties of Non-Split/Split Quantifier Constructions

by Kimiko Nakanishi

Source: Semantics Archive

This dissertation examines the semantics and the syntax-semantics interface properties of constructions involving measurement _ namely, non-split and split quantifier constructions in Japanese and German, and comparative constructions in Japanese and English. One of my central goals is to investigate formal properties of these measurement constructions. I show that these constructions can be categorized into two classes based on Schwarzschildis (2002) notion of emonotonicityi, where a measure function is monotonic relative to the denotation of some element if and only if a measure obtained for that element is larger than a measure obtained for proper subparts of it.

In particular, while non-split quantifier constructions are monotonic to the denotation of a nominal predicate, split quantifier constructions and the relevant comparative constructions are monotonic to the denotation of a verbal predicate. The monotonicity analysis further extends to other cross-linguistic measurement constructions, suggesting that monotonicity is a formal property of a wide range of measurement constructions. The two groups of constructions categorized by monotonicity differ in their domains of measurement: the constructions with nominal monotonicity measure in the nominal domain and the constructions with verbal monotonicity measure in the verbal domain. In split quantifier constructions, the split quantifier syntactically combines with, and semantically operates on, a verbal predicate, yet there is a strong intuition that it somehow measures a nominal predicate as well. This intuition is captured by using a homomorphism (i.e. a structure-preserving mapping) from events to individuals, which makes the split quantifier indirectly measure events by measuring individuals. With this mechanism, it is possible to maintain the compositionality of grammar. Furthermore, the proposed mechanism enables us to satisfactorily account for three characteristic semantic properties of constructions involving measurement in the verbal domain, namely, incompatibility with single-occurrence events, incompatibility with individual-level predicates, and (un)availability of collective readings. The proposed analysis also accounts for the cross-categorial distribution of measure phrases (e.g. two feet of rope, walk two feet, two feet long). A distinction is made between measure phrases and measure functions: while measure phrases are always predicates of scalar intervals (Schwarzschild 2002), measure functions are cross-categorial.

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Posted by Tony Marmo
at 16:45 BST

Updated: Friday, 10 September 2004 16:50 BST