Extended Canonicity of Certain Topological Properties of Set Spaces

摘要

This paper is about the question to what extent the addition of names (of points and sets) to the underlying language increases the expressive power of the modal logic of subset spaces. We ask, in particular, whether or not certain topological properties like separation or connectedness could become canonical then. Our answer is 'yes', if the system is enriched by two pairs of appropriate Gabbay-style rules.