Analogues of Bull’s theorem for hybrid logic

Abstract

Bull’s theorem states that all axiomatic extensions of the modal logic S4.3 have the finite model property. We show that this fails for hybrid logic, by defining an axiomatic extension of the hybrid companion of S4.3, which has only infinite Kripke models. In contrast, by considering hybrid algebraic semantics or, dually, semantics based on two-sorted general frames, we are able to prove analogues of Bull’s theorem for two hybrid languages.