Towards a general theory of action and time
Artificial Intelligence
Journal of Computer and System Sciences
Attributive concept descriptions with complements
Artificial Intelligence
A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
Quantifiers in combinatory PDL: completeness, definability, incompleteness
FCT '85 Fundamentals of Computation Theory
A correspondence theory for terminological logics: preliminary report
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
A Hybrid Treatment of Evolutionary Sets
MICAI '02 Proceedings of the Second Mexican International Conference on Artificial Intelligence: Advances in Artificial Intelligence
Decidable Navigation Logics for Object Structures
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
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
Resolution with Order and Selection for Hybrid Logics
Journal of Automated Reasoning
A dynamic logic for termgraph rewriting
ICGT'10 Proceedings of the 5th international conference on Graph transformations
A tableaux based decision procedure for a broad class of hybrid formulae with binders
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Foundations of instance level updates in expressive description logics
Artificial Intelligence
Sequent calculi and decidability for intuitionistic hybrid logic
Information and Computation
Reasoning about actions using description logics with general TBoxes
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
On the complexity of hybrid logics with binders
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
When model-checking freeze LTL over counter machines becomes decidable
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
A Family of Dynamic Description Logics for Representing and Reasoning About Actions
Journal of Automated Reasoning
Reasoning in description logics: basics, extensions, and relatives
RW'07 Proceedings of the Third international summer school conference on Reasoning Web
Global view on reactivity: switch graphs and their logics
Annals of Mathematics and Artificial Intelligence
Journal of Automated Reasoning
A proof procedure for hybrid logic with binders, transitivity and relation hierarchies
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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Hybrid languages are extended modal languages which can refer to (or even quantify over) states. Such languages are better behaved proof theoretically than ordinary modal languages for they internalize the apparatus of labeled deduction. Moreover, they arise naturally in a variety of applications, including description logic and temporal reasoning. Thus it would be useful to have a map of their complexity-theoretic properties, and this paper provides one. Our work falls into two parts. We first examine the basic hybrid language and its multi-modal and tense logical cousins. We show that the basic hybrid language (and indeed, multi-modal hybrid languages) are no more complex than ordinary uni-modal logic: all have PSPACE-complete K-satisfiability problems. We then show that adding even one nominal to tense logic raises complexity from pspace to EXPTIME. In the second part we turn to stronger hybrid languages in which it is possible to bind nominals. We prove a general expressivity result showing that even the weak form of binding offered by the ↓ operator easily leads to undecidability.