Qualitative Spatial Reasoning with Topological Relations in the Situation Calculus

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We use a qualitative theory of spatial change and illustrate some of the key representational aspects of specifying such a theory using a formalism to reason about action and change; an effort that we regard to be essential toward a general integration of qualitative spatial reasoning with reasoning about the dynamic, causal aspects of spatial change. A topological theory of space, namely the region connection calculus, is used as the spatial metaphor in this work; the reason here primarily being that topological distinctions are inherently qualitative in nature and also because a relational approach as general as the RCC is representative of a similar class of relational techniques in the QSR domain. As such, our results can be easily generalised over a wide range of calculi, encompassing other aspects of space, that are based on similar semantics. The main aim of this paper is to illustrate first ideas on how a causal perspective to qualitative spatial reasoning may be provided using the situation calculus, which is a formalism to reason about dynamically changing domains. The minimalist notions of space and/or spatial dynamics in this paper are based on the hypothesis that it is imperative to approach the problem of the said integration at a elementary level before a higher-level abstraction involving complex actions and events is developed.