Institute of Information Science, Academia Sinica

Convexity predicates and the convex hull operator continue to play an important role in theories of spatial representation and reasoning, yet their first-order axiomatization is still a matter of controversy. In this talk, I will critically assess the standard way of extending mereotopology with a convex hull operator along the lines of Cohn et al. (1997), arguing that the resulting notion of convexity is of limited expressivity. I will then present a new approach to adding convexity to a mereotopological theory with boundary elements by specifying first-order axioms for a binary segment operator. These axioms yield a convex hull operator that supports, not only the basic properties of convex regions, but also complex properties concerning region alignment. I will finally discuss how this new approach can motivate changes to the traditional axioms for the convex hull operator, thereby giving rise to an axiomatic treatment of convexity in a mereotopological context that is both expressive and well suited to automated reasoning applications.