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Narcissists Are Easy, Stepmothers Are Hard

Narcissists Are Easy, Stepmothers Are Hard

  • Daniel Gorín17 &
  • Lutz Schröder17,18 
  • Conference paper
  • 854 Accesses

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7213)

Abstract

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.

Keywords

  • Modal Logic
  • Description Logic
  • Model Property
  • Modal Language
  • Relation Symbol

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. DFKI GmbH, Bremen, Germany

    Daniel Gorín & Lutz Schröder

  2. Department of Computer Science, Universität Bremen, Germany

    Lutz Schröder

Authors
  1. Daniel Gorín
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  2. Lutz Schröder
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Editor information

Editors and Affiliations

  1. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Lars Birkedal

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Gorín, D., Schröder, L. (2012). Narcissists Are Easy, Stepmothers Are Hard. In: Birkedal, L. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2012. Lecture Notes in Computer Science, vol 7213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28729-9_16

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  • DOI: https://doi.org/10.1007/978-3-642-28729-9_16

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