Bisimulation through probabilistic testing
Information and Computation
Terminal coalgebras in well-founded set theory
Theoretical Computer Science
Coalgebraic modal logic: soundness, completeness and decidability of local consequence
Theoretical Computer Science
The Description Logic Handbook
The Description Logic Handbook
PSPACE bounds for rank-1 modal logics
ACM Transactions on Computational Logic (TOCL)
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
On the complexity of hybrid logics with binders
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Optimal tableau algorithms for coalgebraic logics
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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Modal languages are well-known for their robust decidability and relatively low complexity. However, as soon as one adds a self-referencing construct, like hybrid logic's down-arrow binder, to the basic modal language, decidability is lost, even if one restricts binding to a single variable. Here, we concentrate on the latter case and investigate the logics obtained by restricting the nesting depth of modalities between binding and use. In particular, for distances strictly below 3 we obtain well-behaved logics with a relatively high descriptive power. We investigate the fragment with distance 1 in the framework of coalgebraic modal logic, for which we provide very general decidability and complexity results. For the fragment with distance 2 we focus on the case of Kripke semantics and obtain optimum complexity bounds (no harder than the base logic). We show that this fragment is expressive enough to accommodate the guarded fragment over the correspondence language.