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Counting in the Two Variable Guarded Logic with Transitivity

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STACS 2005 (STACS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3404))

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Abstract

We show that the extension of the two-variable guarded fragment with transitive guards (GF+TG) by functionality statements is undecidable. This gives immediately undecidability of the extension of GF+TG by counting quantifiers. The result is optimal, since both the three-variable fragment of the guarded fragment with counting quantifiers and the two-variable guarded fragment with transitivity are undecidable.

We also show that the extension of GF+TG with functionality, where functional predicate letters appear in guards only, is decidable and of the same complexity as GF+TG. This fragment captures many expressive modal and description logics.

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Opole University, Opole, Poland

    Lidia Tendera

Authors
  1. Lidia Tendera
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Editor information

Editors and Affiliations

  1. Universität Stuttgart, FMI, Germany

    Volker Diekert

  2. LIF, CNRS & Univ. de Provence,, Marseille

    Bruno Durand

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Tendera, L. (2005). Counting in the Two Variable Guarded Logic with Transitivity. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_7

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  • DOI: https://doi.org/10.1007/978-3-540-31856-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24998-6

  • Online ISBN: 978-3-540-31856-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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