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Deciding Termination of Query Evaluation in Transitive-Closure Logics for Constraint Databases

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Database Theory — ICDT 2003 (ICDT 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2572))

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Abstract

We study extensions of first-order logic over the reals with different types of transitive-closure operators as query languages for constraint databases that can be described by Boolean combinations of polynomial inequalities over the reals. We are in particular interested in deciding the termination of the evaluation of queries expressible in these transitive-closure logics. It turns out that termination is undecidable in general. However, we show that the termination of the transitive closure of a continuous function graph in the two-dimensional plane, viewed as a binary relation over the reals, is decidable, and even expressible in first-order logic over the reals. Based on this result, we identify a particular transitive-closure logic for which termination of query evaluation is decidable and which is more expressive than first-order logic over the reals. Furthermore, we can define a guarded fragment in which exactly the terminating queries of this language are expressible.

The research presented here was done while this author was at the University of Limburg.

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Author information

Authors and Affiliations

  1. University of Helsinki Helsinki Institute for Information Technology, Teollisuuskatu 23, PO Box 26, Fin-00014, Helsinki, Finland

    Floris Geerts

  2. Dept. of Mathematics, Physics and Computer Science Universitaire Campus, University of Limburg, 3590, Diepenbeek, Belgium

    Bart Kuijpers

Authors
  1. Floris Geerts
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  2. Bart Kuijpers
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Editor information

Editors and Affiliations

  1. Dip. di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Salaria 113, 00198, Roma, Italy

    Diego Calvanese  & Maurizio Lenzerini  & 

  2. Department of Computer Science, Stanford University, Room 474 Gates Computer Science Building 4B, 94305-9045, Stanford, CA, USA

    Rajeev Motwani

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Geerts, F., Kuijpers, B. (2003). Deciding Termination of Query Evaluation in Transitive-Closure Logics for Constraint Databases. In: Calvanese, D., Lenzerini, M., Motwani, R. (eds) Database Theory — ICDT 2003. ICDT 2003. Lecture Notes in Computer Science, vol 2572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36285-1_13

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  • DOI: https://doi.org/10.1007/3-540-36285-1_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00323-6

  • Online ISBN: 978-3-540-36285-2

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