Block-Sorted Quantified Conjunctive Queries

  • Hubie Chen
  • Dániel Marx
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7966)


We study the complexity of model checking in quantified conjunctive logic, that is, the fragment of first-order logic where both quantifiers may be used, but conjunction is the only permitted connective. In particular, we study block-sorted queries, which we define to be prenex sentences in multi-sorted relational first-order logic where two variables having the same sort must appear in the same quantifier block. We establish a complexity classification theorem that describes precisely the sets of block-sorted queries of bounded arity on which model checking is fixed-parameter tractable. This theorem strictly generalizes, for the first time, the corresponding classification for existential conjunctive logic (which is known and due to Grohe) to a logic in which both quantifiers are present.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hubie Chen
    • 1
  • Dániel Marx
    • 2
  1. 1.Universidad del País Vasco and IKERBASQUESan SebastiánSpain
  2. 2.Computer and Automation Research InstituteHungarian Academy of Sciences (MTA SZTAKI)BudapestHungary

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