A Two-Dimensional Hybrid Logic of Subset Spaces

Logics of space typically involve two sorts of entities, points and sets, and so are amenable for investigation using hybrid modal languages with nominals for both sorts. As Hilbert systems for these logics are quite complicated, Gentzen systems are used in this paper, first for the basic two-dimensional hybrid logic and then for the logic of subset spaces, which needs additional rules. This provides a foothold from which to consider extensions to neighborhood and topological logics, and also application fields such as epistemic and doxastic logics.