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International Conference on Logic for Programming Artificial Intelligence and Reasoning

LPAR 2007: Logic for Programming, Artificial Intelligence, and Reasoning pp 318–332Cite as

On Finite Satisfiability of the Guarded Fragment with Equivalence or Transitive Guards

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4790))

Abstract

The guarded fragment of first-order logic, GF, enjoys the finite model property, so the satisfiability and the finite satisfiability problems coincide.

We are concerned with two extensions of the two-variable guarded fragment that do not possess the finite model property, namely, GF2 with equivalence and GF2 with transitive guards. We prove that in both cases every finitely satisfiable formula has a model of at most double exponential size w.r.t. its length.

To obtain the result we invent a strategy of building finite models that are formed from a number of multidimensional grids placed over a cylindrical surface. The construction yields a 2Nexptime -upper bound on the complexity of the finite satisfiability problem for these fragments. For the case with equivalence guards we improve the bound to 2Exptime.

Supported by Polish Ministry of Science and Higher Education research project nr N206 022 31/3660 2006/2009.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław,  

    Emanuel Kieroński

  2. Institute of Mathematics and Informatics, Opole University,  

    Lidia Tendera

Authors
  1. Emanuel Kieroński
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  2. Lidia Tendera
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Nachum Dershowitz Andrei Voronkov

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Kieroński, E., Tendera, L. (2007). On Finite Satisfiability of the Guarded Fragment with Equivalence or Transitive Guards. In: Dershowitz, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2007. Lecture Notes in Computer Science(), vol 4790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75560-9_24

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  • DOI: https://doi.org/10.1007/978-3-540-75560-9_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75558-6

  • Online ISBN: 978-3-540-75560-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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