Hybrid logics: Characterization, interpolation and complexity

Journal of Symbolic Logic 66 (3):977-1010 (2001)
Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called $\mathscr{H}(\downarrow, @)$ . We show in detail that $\mathscr{H}(\downarrow, @)$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of Ehrenfeucht-Fraisse game, and an enriched notion of bisimulation) and a syntactic characterization (in terms of bounded formulas). The key result to emerge is that $\mathscr{H}(\downarrow, @)$ corresponds to the fragment of first-order logic which is invariant for generated submodels. We then show that $\mathscr{H}(\downarrow, @)$ enjoys (strong) interpolation, provide counterexamples for its finite variable fragments, and show that weak interpolation holds for the sublanguage H(@). Finally, we provide complexity results for H(@) and other fragments and variants, and sharpen known undecidability results for $\mathscr{H}(\downarrow, @)$
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DOI 10.2307/2695090
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References found in this work BETA
Modal Logic with Names.George Gargov & Valentin Goranko - 1993 - Journal of Philosophical Logic 22 (6):607 - 636.
Hybrid Languages.Patrick Blackburn & Jerry Seligman - 1995 - Journal of Logic, Language and Information 4 (3):251-272.
Hybrid Languages and Temporal Logic.P. Blackburn & M. Tzakova - 1999 - Logic Journal of the IGPL 7 (1):27-54.
Hybrid Completeness.P. Blackburn & M. Tzakova - 1998 - Logic Journal of the IGPL 6 (4):625-650.

View all 6 references / Add more references

Citations of this work BETA
Arthur Prior and Hybrid Logic.Patrick Blackburn - 2006 - Synthese 150 (3):329-372.
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