Hybrid Logic Meets IF Modal Logic |
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Authors: | Tero Tulenheimo |
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Affiliation: | 1. Department of Philosophy, University of Helsinki, P.O. Box 9, Siltavuorenpenger 20 A, 00014, Helsinki, Finland
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Abstract: | 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. |
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