Geometric Model Checking of Continuous Space

Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Logic Closure Spaces, SLCS, extends with reachability connectives that, in turn, can be used expressing interesting spatial properties, such as "being near to" or surrounded by". SLCS constitutes kernel solid logical framework reasoning about discrete space, graphs and digital images, interpreted quasi closure spaces. Following recently geometric semantics Logic, we propose an continuous admitting procedure, by resorting to models based on polyhedra. Such representations space increasingly relevant many domains application, due developments 3D scanning visualisation that exploit mesh processing. We introduce PolyLogicA, checker formulas polyhedra demonstrate feasibility our approach two polyhedral realistic size. Finally, definition bisimilarity, proving it characterises equivalence.