Vector Space Semantics: A Model-Theoretic Analysis of Locative Prepositions

This paper introduces a compositional semantics of locative prepositional phrases which is based on a vector space ontology. Model-theoretic properties of prepositions like monotonicity and conservativity are defined in this system in a straightforward way. These notions are shown to describe central inferences with spatial expressions and to account for the grammaticality of preposition modification. Model-theoretic constraints on the set of possible prepositions in natural language are specified, similar to the semantic universals of Generalized Quantifier Theory.