Measure Phrase Modification in Vector Space Semantics

This paper argues for a general principle that governs the meaning and acceptability of measure phrase modification with locative prepositions, degree adjectives and comparatives. Following previous work by Zwarts and Faller, structures such as two meters behind the house, five years old and three cm. shorter than Mary are all analyzed using intersective modification of predicates over vectors. The unacceptability of structures such as *two meters on the house and *five years old is analyzed in a unified manner, as a result of the monotonicity properties of the set of vectors that the modified item denotes. According to the proposed condition, modification with measure phrases allows only sets of vectors that are both upward and downward monotone, in a way that rules out expressions with empty denotations.