A Road-Map on Complexity for Hybrid Logics

13 years 8 months ago

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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 res...

Carlos Areces, Patrick Blackburn, Maarten Marx

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