Satisfiability of a spatial logic with tree variables

  • Authors:

  • Emmanuel Filiot;Jean-Marc Talbot;Sophie Tison

  • Affiliations:

  • INRIA Futurs, University of Lille 1, LIFL, UMR, CNRS;University of Provence, LIF, UMR, CNRS, Marseille;INRIA Futurs, University of Lille 1, LIFL, UMR, CNRS

  • Venue:
  • CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
  • Year:
  • 2007

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Abstract

We investigate in this paper the spatial logic TQL for querying semistructured data, represented as unranked ordered trees over an infinite alphabet. This logic consists of usual Boolean connectives, spatial connectives (derived from the constructors of a tree algebra), tree variables and a fixpoint operator for recursion. Motivated by XML-oriented tasks, we investigate the guarded TQL fragment. We prove that for closed formulas this fragment is MSO-complete. In presence of tree variables, this fragment is strictly more expressive than MSO as it allows for tree (dis)equality tests, i.e. testing whether two subtrees are isomorphic or not. We devise a new class of tree automata, called TAGED, which extends tree automata with global equality and disequality constraints. We show that the satisfiability problem for guarded TQL formulas reduces to emptiness of TAGED. Then, we focus on bounded TQL formulas: intuitively, a formula is bounded if for any tree, the number of its positions where a subtree is captured by a variable is bounded. We prove this fragment to correspond with a subclass of TAGED, called bounded TAGED, for which we prove emptiness to be decidable. This implies the decidability of the bounded guarded TQL fragment. Finally, we compare bounded TAGED to a fragment of MSO extended with subtree isomorphism tests.