Hybrid Logic Meets IF Modal Logic

The hybrid logic H(@,ˉ){mathcal{H}(@,downarrow)} and the independence friendly modal logic IFML are compared for their expressive powers. We introduce a logic IFML _c having a non-standard syntax and a compositional semantics; in terms of this logic a syntactic fragment of IFML is singled out, denoted IFML _c . (In the Appendix it is shown that the game-theoretic semantics of IFML _c coincides with the compositional semantics of IFML _c .) The hybrid logic H(@,ˉ){mathcal{H}(@,downarrow)} is proven to be strictly more expressive than IFML _c . By contrast, H(@,ˉ){mathcal{H}(@,downarrow)} and the full IFML are shown to be incomparable for their expressive powers. Building on earlier research (Tulenheimo and Sevenster 2006), a PSPACE-decidable fragment of the undecidable logic H(@,ˉ){mathcal{H}(@,downarrow)} is disclosed. This fragment is not translatable into the hybrid logic H(@){mathcal{H}(@)} and has not been studied previously in connection with hybrid logics. In the Appendix IFML _c is shown to lack the property of ‘quasi-positionality’ but proven to enjoy the weaker property of ‘bounded quasi-positionality’. The latter fact provides from the IFML internal perspective an account of what makes the compositional semantics of IFML _c possible.