Qualitative Spatial Reasoning Using Algebraic Topology

Many propositions in spatial and qualitative reasoning can be modelled as regions in phase or con guration spaces Deciding the consistency of k propositions then amounts to deciding the question of whether there exists a point which simultaneously falls into all k corre sponding regions A more di cult problem is to decide whether there is a point which falls only within the given k regions I call this feasibility of the set of propositions In this paper I present a method for deciding consistency and feasibil ity for convex regions using only topological inference It uses Helly s theorem to decide consistency of any set of k propositions based on in formation about consistency of small subsets Using methods of algebraic topology I show a su cient method to compute a minimal skeleton of feasible places which accurately models the connectivity between feasible environments The method has been implemented I show how to formulate and solve the piano movers problem an important problem in spatial reasoning