Diagrammatic Semantics for Spatial Prepositions

Attempts to use images as mental models of natural language sentences with spatial prepositions have been hindered by differences in level of detail between propositional and diagrammtic representations. Specifically, when propositional knowledge is modeled with an image, the level of detail of the diagrammatic representation often requires some details to be assumed. Subsequently, it becomes unclear what details in an image are necessary versus arbitrary; this is the Indeterminacy Problem. Previously, a computational model of imagery, ISR, was introduced that can avoid the Indeterminacy Problem by dynamically manipulating images, rather than treating them as static models. This paper reports our attempts to apply ISR in a fairly realistic domain in which spatial prepositions are used to relate the locations of objects in a room. The major difficulty encountered was in modeling the constraints of gravity, and the analysis of this problem exposes a subtle but crucial interaction among various components of ISR. We describe a heuristic solution, and suggest, by similarity to planning, that natural language semantic processors require such heuristics that trade completeness for speed.