Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-t4qhp Total loading time: 0.368 Render date: 2022-08-10T12:52:30.905Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Finite model reasoning over existential rules*

Published online by Cambridge University Press:  24 August 2017

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)

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.

Type
Regular Papers
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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, 16201654.CrossRefGoogle Scholar
Bárány, V., Gottlob, G. and Otto, M. 2014. Querying the guarded fragment. Logical Methods in Computer Science 10, 2, 135.CrossRefGoogle 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, 33:133:44.CrossRefGoogle Scholar
Bourhis, P., Manna, M., Morak, M. and Pieris, A. 2016. Guarded-based disjunctive tuple-generating dependencies. ACM TODS 41, 4, 27:127:45.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, 115174.Google 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.Google 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, 5783.CrossRefGoogle Scholar
Calì, A., Gottlob, G. and Pieris, A. 2010. Advanced processing for ontological queries. PVLDB 3, 1, 554565.Google Scholar
Calì, A., Gottlob, G. and Pieris, A. 2012. Towards more expressive ontology languages: The query answering problem. Artificial Intelligence Journal 193, 87128.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, 95103.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, 425444.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, 89124.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, 180206.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, 4259.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, 877892.CrossRefGoogle Scholar
Gottlob, G., Orsi, G. and Pieris, A. 2014. Query rewriting and optimization for ontological databases. ACM TODS 39, 3, 25:125:46.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, 167189.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.Google Scholar
Rosati, R. 2007. The limits of querying ontologies. In Proc. of ICDT'07, 164–178.Google Scholar
Supplementary material: PDF

Amendola et al supplementary material

Online Appendix

Download Amendola et al supplementary material(PDF)
PDF 150 KB

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Finite model reasoning over existential rules*
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Finite model reasoning over existential rules*
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Finite model reasoning over existential rules*
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *