Geometrical concepts at the interface of formal and cognitive models

The paper has two related aims. One is to outline a proposal for a spatially motivated model of discourse, called Discourse Space Theory. The other is to use this framework to explore, in a relatively formalised way, the spatial basis of the conceptual complexities arising in the uses of the English progressive verb form (be+-ing). The theory utilises an abstract space in three dimensions (time, space and modality). Verb stems are associated with Aktionsart schemas; aspectual forms like the progressive are viewed as operations on these schemas. The proposal is that geometric concepts, specifically coordinate systems and vectors, can provide a motivated formalism for investigating conceptual structures generated by a human discourse processor.