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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.

References

Baader, F., Calvanese, D., McGuinness, D. L., Nardi, D. and Patel-Schneider, P. F., Eds. 2003. The Description Logic Handbook: Theory, Implementation, and Applications. CUP.Google Scholar
Baget, J., Leclère, M. and Mugnier, M. 2010. Walking the decidability line for rules with existential variables. In Proc. of KR'10.Google Scholar
Baget, J., Leclère, M., Mugnier, M. and Salvat, E. 2009. Extending decidable cases for rules with existential variables. In Proc. of IJCAI'09, 677–682.Google Scholar
Baget, J., Leclère, M., Mugnier, M. and Salvat, E. 2011. On rules with existential variables: Walking the decidability line. Artificial Intelligence Journal 175, 9–10, 1620–1654.CrossRefGoogle Scholar
Bárány, V., Gottlob, G. and Otto, M. 2014. Querying the guarded fragment. Logical Methods in Computer Science 10, 2, 1–35.Google Scholar
Bienvenu, M., ten Cate, B., Lutz, C. and Wolter, F. 2014. Ontology-based data access: A study through disjunctive datalog, csp, and MMSNP. ACM TODS 39, 4, 33:1–33:44.CrossRefGoogle Scholar
Bourhis, P., Manna, M., Morak, M. and Pieris, A. 2016. Guarded-based disjunctive tuple-generating dependencies. ACM TODS 41, 4, 27:1–27:45.CrossRefGoogle Scholar
Calì, A., Gottlob, G. and Kifer, M. 2013. Taming the infinite chase: Query answering under expressive relational constraints. Journal of Artificial Intelligence Research (JAIR) 48, 115–174.CrossRefGoogle Scholar
Calì, A., Gottlob, G. and Lukasiewicz, T. 2009a. Datalog±: A unified approach to ontologies and integrity constraints. In Proc. of ICDT'09, 14–30.Google Scholar
Calì, A., Gottlob, G. and Lukasiewicz, T. 2009b. Tractable query answering over ontologies with datalog+/-. In Proc. of DL'09.CrossRefGoogle Scholar
Calì, A., Gottlob, G. and Lukasiewicz, T. 2012. A general datalog-based framework for tractable query answering over ontologies. Journal of Web Semantics 14, 57–83.CrossRefGoogle Scholar
Calì, A., Gottlob, G. and Pieris, A. 2010. Advanced processing for ontological queries. PVLDB 3, 1, 554–565.Google Scholar
Calì, A., Gottlob, G. and Pieris, A. 2012. Towards more expressive ontology languages: The query answering problem. Artificial Intelligence Journal 193, 87–128.CrossRefGoogle Scholar
Civili, C. and Rosati, R. 2012. A broad class of first-order rewritable tuple-generating dependencies. In Proc. of Datalog 2.0, 68–80.Google Scholar
Deutsch, A., Nash, A. and Remmel, J. B. 2008. The chase revisited. In Proc. of PODS'08, 149–158.Google Scholar
Ebbinghaus, H.-D. and Flum, J. 1995. Satisfiability in the Finite. Springer, Berlin Heidelberg, 95–103.Google Scholar
Fages, F. 1991. A new fixpoint semantics for general logic programs compared with the well-founded and the stable model semantics. New Generation Computing 9, 3/4, 425–444.CrossRefGoogle Scholar
Fagin, R., Kolaitis, P. G., Miller, R. J. and Popa, L. 2005. Data exchange: Semantics and query answering. Theoretical Computer Science 336, 1, 89–124.CrossRefGoogle Scholar
Gogacz, T. and Marcinkowski, J. 2013. Converging to the chase – A tool for finite controllability. In Proc. of LICS'13, 540–549.Google Scholar
Gogacz, T. and Marcinkowski, J. 2017. Converging to the chase – A tool for finite controllability. Journal of Computer and System Sciences 83, 1, 180–206.CrossRefGoogle Scholar
Gottlob, G., Kikot, S., Kontchakov, R., Podolskii, V. V., Schwentick, T. and Zakharyaschev, M. 2014. The price of query rewriting in ontology-based data access. Artificial Intelligence Journal 213, 42–59.CrossRefGoogle Scholar
Gottlob, G., Manna, M. and Pieris, A. 2013. Combining decidability paradigms for existential rules. Theory and Practice of Logic Programming 13, 4–5, 877–892.CrossRefGoogle Scholar
Gottlob, G., Orsi, G. and Pieris, A. 2014. Query rewriting and optimization for ontological databases. ACM TODS 39, 3, 25:1–25:46.CrossRefGoogle Scholar
Gottlob, G., Pieris, A. and Tendera, L. 2013. Querying the guarded fragment with transitivity. In Proc. of ICALP'13, 287–298.Google Scholar
Johnson, D. S. and Klug, A. C. 1984. Testing containment of conjunctive queries under functional and inclusion dependencies. Journal of Computer and System Sciences 28, 1, 167–189.CrossRefGoogle Scholar
Krötzsch, M. and Rudolph, S. 2011. Extending decidable existential rules by joining acyclicity and guardedness. In Proc. of IJCAI'11, 963–968.Google Scholar
Leone, N., Manna, M., Terracina, G. and Veltri, P. 2012. Efficiently computable datalog∃ programs. In Proc. of KR'12.Google Scholar
Rosati, R. 2006. On the decidability and finite controllability of query processing in databases with incomplete information. In Proc. of PODS'06.CrossRefGoogle Scholar
Rosati, R. 2007. The limits of querying ontologies. In Proc. of ICDT'07, 164–178.Google Scholar
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