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On the Satisfiability of Two-Variable Logic over Data Words

  • Conference paper
Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6397))

Abstract

Data trees and data words have been studied extensively in connection with XML reasoning. These are trees or words that, in addition to labels from a finite alphabet, carry labels from an infinite alphabet (data). While in general logics such as MSO or FO are undecidable for such extensions, decidablity results for their fragments have been obtained recently, most notably for the two-variable fragments of FO and existential MSO. The proofs, however, are very long and nontrivial, and some of them come with no complexity guarantees. Here we give a much simplified proof of the decidability of two-variable logics for data words with the successor and data-equality predicates. In addition, the new proof provides several new fragments of lower complexity. The proof mixes database-inspired constraints with encodings in Presburger arithmetic.

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Authors and Affiliations

  1. School of Informatics, University of Edinburgh, UK

    Claire David, Leonid Libkin & Tony Tan

Authors
  1. Claire David
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  2. Leonid Libkin
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  3. Tony Tan
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Editor information

Editors and Affiliations

  1. Institut für Computersprachen 185.2, Theory and Logic Group, TU Wien, Favoritenstraße 9-11, A-1040, Vienna, Austria

    Christian G. Fermüller

  2. School of Computer Science, University of Manchester, Oxford Road, Kilburn Building, M13 9PL, Manchester, United Kingdom

    Andrei Voronkov

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David, C., Libkin, L., Tan, T. (2010). On the Satisfiability of Two-Variable Logic over Data Words. In: Fermüller, C.G., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2010. Lecture Notes in Computer Science, vol 6397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16242-8_18

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  • DOI: https://doi.org/10.1007/978-3-642-16242-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16241-1

  • Online ISBN: 978-3-642-16242-8

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