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Implication and axiomatization of functional and constant constraints

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Abstract

Akhtar et al. introduced equality-generating constraints and functional constraints as a first step towards dependency-like integrity constraints for RDF data [3]. Here, we focus on functional constraints. Since the usefulness of functional constraints is not limited to the RDF data model, we study the functional constraints in the more general setting of relations with arbitrary arity. We further introduce constant constraints and study the functional and constant constraints combined. Our main results are sound and complete axiomatizations for the functional and constant constraints, both separately and combined. These axiomatizations are derived using the chase algorithm for equality-generating constraints. For derivations of constant constraints, we show how every chase step can be simulated by a bounded number of applications of inference rules. For derivations of functional constraints, we show that the chase algorithm can be normalized to a more specialized symmetry-preserving chase algorithm performing so-called symmetry-preserving steps. We then show how each symmetry-preserving step can be simulated by a bounded number of applications of inference rules. The axiomatization for functional constraints is in particular applicable to the RDF data model, solving a major open problem of Akhtar et al.

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Authors and Affiliations

  1. Faculty of Sciences, Hasselt University and Transnational University of Limburg, Martelarenlaan 42, 3500, Hasselt, Belgium

    Jelle Hellings & Marc Gyssens

  2. Department of Mathematics and Computer Science, University of Antwerp, Campus Middelheim, Bldg. G, Middelheimlaan 1, 2020, Antwerp, Belgium

    Jan Paredaens

  3. Computer Science Department, Pomona College, 185 E. 6th St., Claremont, CA, 91711, USA

    Yuqing Wu

Authors
  1. Jelle Hellings
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  2. Marc Gyssens
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  3. Jan Paredaens
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  4. Yuqing Wu
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Correspondence to Jelle Hellings.

Additional information

This is a revised and extended version of the paper ‘Implication and Axiomatization of Functional Constraints on Patterns with an Application to the RDF Data Model’ presented at the 8th International Symposium on Foundations of Information and Knowledge Systems, Bordeaux, France (FOIKS 2014) [25].

Yuqing Wu carried out part of her work during a sabbatical visit to Hasselt University with a Senior Visiting Postdoctoral Fellowship of the Research Foundation Flanders (FWO).

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Hellings, J., Gyssens, M., Paredaens, J. et al. Implication and axiomatization of functional and constant constraints. Ann Math Artif Intell 76, 251–279 (2016). https://doi.org/10.1007/s10472-015-9473-7

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  • DOI: https://doi.org/10.1007/s10472-015-9473-7

Keywords

Mathematics Subject Classfication (2010)

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