A modular bisimulation characterisation for fragments of hybrid logic

Abstract

There are known characterisations of several fragments of hybrid logic by means of invariance under bisimulations of some kind. The fragments include $\{\store, \jump\}$ with or without nominals (Areces, Blackburn, Marx), $\jump$ with or without nominals (ten Cate), and $\store$ without nominals (Hodkinson, Tahiri). Some pairs of these characterisations, however, are incompatible with one another. For other fragments of hybrid logic no such characterisations were known so far. We prove a generic bisimulation characterisation theorem for all standard fragments of hybrid logic, in particular for the case with $\store$ and nominals, left open by Hodkinson and Tahiri. Our characterisation is built on a common base and for each feature extension adds a specific condition, so it is modular in an engineering sense.