A Semantic Characterization of Locative PPs

The last two decades have seen remarkable development in compositional modeltheoretic semantics of natural language. The idea that natural language expressions can be directly interpreted in the model of discourse has gained significant support in various domains. It led to a better understanding of inference in linguistics with close relation to syntax, helped to characterize linguistically relevant classes of expressions, and revealed systematic constraints on their possible meanings. Quite independently of these developments, much work in the fields of cognitive and conceptual semantics has acquired a significant body of knowledge about the semantic behaviour of prepositional phrases (PPs). In the modeltheoretic framework, however, the semantics of PPs has remained, to a large extent, unexplored. Our aim in this paper is to contribute for bridging this gap. We refine and extend the proposal in Zwarts (1995), arguing for a vector space as the underlying ontology in the compositional analysis of locative PP structures. In section 2 we introduce a general semantic framework that uses such a model. Section 3 studies some denotational properties of prepositions in the proposed system. Certain properties introduced in Zwarts (1995) will be placed here in a wider perspective of preposition monotonicity. Two notions of monotonicity are defined and shown to be linguistically relevant in restricting the set of possible preposition denotations, accounting for central inferences and affecting grammaticality of modified PPs. An additional constraint, similar to the conservativity restriction on determiners, is shown to hold of natural language locative prepositions. Throughout this paper, we presuppose familiarity with basic Linear Algebra and simple notions from Topology.1 Some useful definitions are summarized in an appendix.