Modelling the semantic variability of spatial prepositions in referring expressions

Spatial prepositions in the English language can be used to denote a vast array of configurations which may greatly diverge from any canonical meaning and this semantic variability poses challenges for many systems where commands or queries are given in natural language. There have been many accounts from Linguistics and Cognitive Science highlighting the various phenomena which contribute to this semantic variability --- primarily, spatial prepositions appear to encode functional as well as spatial information and to also exhibit polysemy. Both these issues represent significant challenges for grounded natural language systems and have not yet been accounted for in semantic models of spatial language. To begin exploring the semantic variability of spatial prepositions, I will compare various cognitive accounts which incorporate the functional notions of support and location control and I will provide methods for constructing a semantic model based on Prototype Theory. In order to incorporate polysemy into this model, I will contribute methods for identifying polysemes based on Herskovits' notion of `ideal meanings' as well as a modification of the `principled polysemy' framework of Tyler and Evans. I will also introduce a notion of `polyseme hierarchy' which will allow these polysemes to be incorporated in the semantic model. By including functional relationships as well as polysemy into a semantic model we are able to provide a measure of typicality which is useful in interpreting referring expressions. However, this model does not yet account for `object-specific features' which seem to influence categorisation decisions involving spatial prepositions. In the final chapter I will provide insight into the nature of categorisation and typicality for spatial prepositions and highlight the importance of object-specific features. Though a concrete solution to including these features will not be provided, I will provide suggestions of how these features may be included in our semantic model