Experiments in Theorem Proving for Topological Hybrid Logic

This paper discusses two experiments in theorem proving for hybrid logic under the topological interpretation. We begin by discussing the topological interpretation of hybrid logic and noting what it adds to the topological interpretation of orthodox modal logic. We then examine two implemented proof methods. The first makes use of HyLoBan, a terminating theorem prover that searches for a winning search strategy in certain topologically motivated games. The second is a translation-based approach that makes use HyLoTab [J. van Eijck. HyLoTab — Tableau-based theorem proving for hybrid logics. Manuscript, CWI, available from http://www.cwi.nl/~jve/hylotab, 2002], a tableaux-based theorem prover for hybrid logic under the standard relational interpretation. We compare the two methods, and note a number of directions for further work.