Cellular ontology as a basis for spatiotemporal reasoning

A logic for reasoning about dynamic systems should be defined on three levels. The material level is expressed in quantitative terms, the image level defines models in terms of discrete mathematics, and the logic level defines the logical language and deduction system. Consider the problem of guiding a vehicle that has to move within severe spatial constraints. For a simple version of a cellular ontology, the material level is a 2D surface where vehicles move along trajectories formed from straight-line segments and circular arcs which are each others' tangents at the points of transition. The image level is obtained by dividing the surface into equally-sized cells, which may be, for example, quadratic or hexagonal. For a given cell structure, with a finite set of ports and a finite set of orientations, and allowing also for some restrictions on vehicle movements, we obtain a finite set of possible maneuvers. It is therefore possible to calculate in advance a qualitative information structure that can be used for analyzing and planning the movements of a vehicle in the cellular driving space.