Hybrid Logic Meets IF Modal Logic

• Authors: Tero Tulenheimo
• Venue: Journal of Logic, Language and Information
• Year: 2009

The hybrid logic $${\mathcal{H}(@,\downarrow)}$$ 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 $${\mathcal{H}(@,\downarrow)}$$ is proven to be strictly more expressive than IFML c . By contrast, $${\mathcal{H}(@,\downarrow)}$$ 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 $${\mathcal{H}(@,\downarrow)}$$ is disclosed. This fragment is not translatable into the hybrid logic $${\mathcal{H}(@)}$$ 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.