A Spatial Similarity Measure based on Games: Theory and Practice

Model comparison games can be used not only to decide whether two specific models are equivalent or not, but also to establish a measurement of difference among a whole class of models. We show how this is possible in the case of the spatial modal logic S4u of Bennett. The approach results in a spatial similarity measure based on topological model comparison games. After establishing the theoretical framework, we move towards practice by giving an algorithm to effectively compute the similarity measure for a class of topological models widely used in computer science applications: polygons of the real plane. In the appendix, we briefly overview an implemented system based on the theoretical framework.