An analogue of Bull's theorem for Hybrid Logic

Abstract

Hybrid logic extends modal logic with a special sort of variables, called nominals, which are evaluated to singletons in Kripke models by valuations, thus acting as names for states in models. Various syntactic mechanisms for exploiting and enhancing the expressive power gained through the addition of nominals can be included, most characteristically the satisfaction operator, @_ip, allowing one to express that p holds at the world named by a nominal i.R.A. Bull famously proved that each normal extension of S4.3 has the finite modelproperty. In the current paper, we prove a hybrid analogue of Bull's result. Like the proof of Bull's original result, ours is algebraic, and thus our secondary aim with this work is to illustrate the usefulness of algebraic methods within hybrid logic research, a field where such methods have been largely ignored.