A Road-Map on Complexity for Hybrid Logics

  • Carlos Areces
  • Patrick Blackburn
  • Maarten Marx
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1683)


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.


Computational Complexity Modal and Temporal Logic Description Logic Labeled Deduction 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Carlos Areces
    • 1
  • Patrick Blackburn
    • 2
  • Maarten Marx
    • 3
  1. 1.ILLC. UvAPlantageThe Netherlands
  2. 2.ComputerlinguistikUniversität des SaarlandesSaarbrückenGermany
  3. 3.Department of Artificial IntelligenceFree University, Amsterdam, and ILLC. UvAPlantage Muidergracht 24The Netherlands

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