Journal of Logic, Language and Information

, Volume 18, Issue 4, pp 559-591

First online:

Hybrid Logic Meets IF Modal Logic

  • Tero TulenheimoAffiliated withDepartment of Philosophy, University of Helsinki Email author 

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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.


Compositionality Decidability Expressive power Game-theoretic semantics Hybrid logic Independence friendly logic Modal logic