Journal of Logic, Language and Information

, Volume 18, Issue 4, pp 559–591

Hybrid Logic Meets IF Modal Logic

Article

DOI: 10.1007/s10849-009-9092-y

Cite this article as:
Tulenheimo, T. J of Log Lang and Inf (2009) 18: 559. doi:10.1007/s10849-009-9092-y

Abstract

The hybrid logic \({\mathcal{H}(@,\downarrow)}\) and the independence friendly modal logic IFML are compared for their expressive powers. We introduce a logic IFMLc having a non-standard syntax and a compositional semantics; in terms of this logic a syntactic fragment of IFML is singled out, denoted IFMLc. (In the Appendix it is shown that the game-theoretic semantics of IFMLc coincides with the compositional semantics of IFMLc.) The hybrid logic \({\mathcal{H}(@,\downarrow)}\) is proven to be strictly more expressive than IFMLc. 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 IFMLc 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 IFMLc possible.

Keywords

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

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of HelsinkiHelsinkiFinland