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Characterizing Boundedness in Chase Variants

Published online by Cambridge University Press:  04 June 2020

STATHIS DELIVORIASOpen the ORCID record for STATHIS DELIVORIAS[Opens in a new window],
MICHEL LECLÈRE,
MARIE-LAURE MUGNIER and
FEDERICO ULLIANA
STATHIS DELIVORIAS
Affiliation:
University of Montpellier, LIRMM, CNRS, INRIA, Montpellier, France, (e-mails: jazzcrazysta@yahoo.com, mugnier@lirmm.fr, leclere@lirmm.fr, federico.ulliana@lirmm.fr)
MICHEL LECLÈRE
Affiliation:
University of Montpellier, LIRMM, CNRS, INRIA, Montpellier, France, (e-mails: jazzcrazysta@yahoo.com, mugnier@lirmm.fr, leclere@lirmm.fr, federico.ulliana@lirmm.fr)
MARIE-LAURE MUGNIER
Affiliation:
University of Montpellier, LIRMM, CNRS, INRIA, Montpellier, France, (e-mails: jazzcrazysta@yahoo.com, mugnier@lirmm.fr, leclere@lirmm.fr, federico.ulliana@lirmm.fr)
FEDERICO ULLIANA
Affiliation:
University of Montpellier, LIRMM, CNRS, INRIA, Montpellier, France, (e-mails: jazzcrazysta@yahoo.com, mugnier@lirmm.fr, leclere@lirmm.fr, federico.ulliana@lirmm.fr)
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Abstract

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Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions.

Keywords

knowledge representation and nonmonotonic reasoninglogic programming methodology and applicationsdatabases and semantic web reasoningtheory

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