An Applied Calculus for Spatial Accessibility Reasoning

Recent attempts to perform formal knowledge representation and reasoning in cell biology have presented new challenges to spatial reasoning. In this paper we formalize two distinct notions of containment that were so motivated and which are relevant to reasoning about physical systems, a notion of being inside and a notion of being restricted. We develop a formal vocabulary for purposes of representing and reasoning about restrictive containment and formalize three kinds of accessibility that are each salient to attempts to reason about the possibility of interaction between pairs of objects in a system. We also consider the relation of this calculus to the well known Region Connection Calculus and related calculi for reasoning about containment. Finally, we discuss methods for implementing in a context of uncertainty, within a planning system and discuss an application to some simple representation and reasoning tasks in virology.