Reasoning about operations on sets

Abstract

The present paper is about a framework of formal topological reasoning originating from the fundamental work of Moss and Parikh relating to this. We add a set of unary operators involving sets to that system. This new means of expression gives us considerably more expressive power with regard to spatial operations, but the accompanying logic remains sound and semantically complete with respect to the class of all subset spaces that are enriched accordingly. Moreover, the new logic turns out to be decidable. We prove these results by relying heavily on a particular extension of the common modal formalism, viz hybrid logic. © Springer-Verlag Berlin Heidelberg 2007.