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Finite model reasoning over existential rules*

Published online by Cambridge University Press:  24 August 2017

GIOVANNI AMENDOLA Open the ORCID record for GIOVANNI AMENDOLA [Opens in a new window] ,
NICOLA LEONE  and
MARCO MANNA
GIOVANNI AMENDOLA
Affiliation:
Department of Mathematics and Computer Science, University of Calabria, Via Pietro Bucci, 87036 Arcavacata, Rende, Cosenza, Italy (e-mails: amendola@mat.unical.it, leone@mat.unical.it, manna@mat.unical.it)
NICOLA LEONE
Affiliation:
Department of Mathematics and Computer Science, University of Calabria, Via Pietro Bucci, 87036 Arcavacata, Rende, Cosenza, Italy (e-mails: amendola@mat.unical.it, leone@mat.unical.it, manna@mat.unical.it)
MARCO MANNA
Affiliation:
Department of Mathematics and Computer Science, University of Calabria, Via Pietro Bucci, 87036 Arcavacata, Rende, Cosenza, Italy (e-mails: amendola@mat.unical.it, leone@mat.unical.it, manna@mat.unical.it)
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Abstract

Ontology-based query answering asks whether a Boolean conjunctive query is satisfied by all models of a logical theory consisting of a relational database paired with an ontology. The introduction of existential rules (i.e., Datalog rules extended with existential quantifiers in rule heads) as a means to specify the ontology gave birth to Datalog+/-, a framework that has received increasing attention in the last decade, with focus also on decidability and finite controllability to support effective reasoning. Five basic decidable fragments have been singled out: linear, weakly acyclic, guarded, sticky, and shy. Moreover, for all these fragments, except shy, the important property of finite controllability has been proved, ensuring that a query is satisfied by all models of the theory iff it is satisfied by all its finite models. In this paper, we complete the picture by demonstrating that finite controllability of ontology-based query answering holds also for shy ontologies, and it therefore applies to all basic decidable Datalog+/- classes. To make the demonstration, we devise a general technique to facilitate the process of (dis)proving finite controllability of an arbitrary ontological fragment.

Keywords

existential rulesDatalogfinite controllabilityfinite model reasoningquery answering
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 17 , Special Issue 5-6: 33rd International Conference on Logic Programming , September 2017 , pp. 726 - 743
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

*

The paper has been partially supported by the Italian Ministry for Economic Development (MISE) under project “PIUCultura – Paradigmi Innovativi per l'Utilizzo della Cultura” (n. F/020016/01-02/X27), and under project “Smarter Solutions in the Big Data World (S2BDW)” (n. F/050389/01-03/X32) funded within the call “HORIZON2020” PON I&C 2014-2020.

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