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A Road-Map on Complexity for Hybrid Logics

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Computer Science Logic (CSL 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1683))

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Abstract

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.

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Author information

Authors and Affiliations

  1. ILLC. UvA, Plantage, Muidergracht 24, 1018TV, The Netherlands

    Carlos Areces

  2. Computerlinguistik, Universität des Saarlandes, D-66041, Saarbrücken, Germany

    Patrick Blackburn

  3. Department of Artificial Intelligence, Free University, Amsterdam, and ILLC. UvA, Plantage Muidergracht 24, 1018TV, The Netherlands

    Maarten Marx

Authors
  1. Carlos Areces
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  2. Patrick Blackburn
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  3. Maarten Marx
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Editor information

Editors and Affiliations

  1. Mathematisches Institut, Universität Freiburg, Eckerstr. 1, D-79104, Freiburg, Germany

    Jörg Flum

  2. Dpto. de Sistemas Informáticos y Programación Edificio Fac. Matemáticas, Universidad Complutense de Madrid, Av. Complutense s/n, E-28040, Madrid, Spain

    Mario Rodriguez-Artalejo

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© 1999 Springer-Verlag Berlin Heidelberg

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Areces, C., Blackburn, P., Marx, M. (1999). A Road-Map on Complexity for Hybrid Logics. In: Flum, J., Rodriguez-Artalejo, M. (eds) Computer Science Logic. CSL 1999. Lecture Notes in Computer Science, vol 1683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48168-0_22

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  • DOI: https://doi.org/10.1007/3-540-48168-0_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66536-6

  • Online ISBN: 978-3-540-48168-3

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