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Finite model reasoning over existential rules*


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.

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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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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.
Baget, J., Leclère, M. and Mugnier, M. 2010. Walking the decidability line for rules with existential variables. In Proc. of KR'10.
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.
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.
Bárány, V., Gottlob, G. and Otto, M. 2014. Querying the guarded fragment. Logical Methods in Computer Science 10, 2, 135.
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.
Bourhis, P., Manna, M., Morak, M. and Pieris, A. 2016. Guarded-based disjunctive tuple-generating dependencies. ACM TODS 41, 4, 27:127:45.
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.
Calì, A., Gottlob, G. and Lukasiewicz, T. 2009a. Datalog±: A unified approach to ontologies and integrity constraints. In Proc. of ICDT'09, 14–30.
Calì, A., Gottlob, G. and Lukasiewicz, T. 2009b. Tractable query answering over ontologies with datalog+/-. In Proc. of DL'09.
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.
Calì, A., Gottlob, G. and Pieris, A. 2010. Advanced processing for ontological queries. PVLDB 3, 1, 554565.
Calì, A., Gottlob, G. and Pieris, A. 2012. Towards more expressive ontology languages: The query answering problem. Artificial Intelligence Journal 193, 87128.
Civili, C. and Rosati, R. 2012. A broad class of first-order rewritable tuple-generating dependencies. In Proc. of Datalog 2.0, 68–80.
Deutsch, A., Nash, A. and Remmel, J. B. 2008. The chase revisited. In Proc. of PODS'08, 149–158.
Ebbinghaus, H.-D. and Flum, J. 1995. Satisfiability in the Finite. Springer, Berlin Heidelberg, 95103.
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.
Fagin, R., Kolaitis, P. G., Miller, R. J. and Popa, L. 2005. Data exchange: Semantics and query answering. Theoretical Computer Science 336, 1, 89124.
Gogacz, T. and Marcinkowski, J. 2013. Converging to the chase – A tool for finite controllability. In Proc. of LICS'13, 540–549.
Gogacz, T. and Marcinkowski, J. 2017. Converging to the chase – A tool for finite controllability. Journal of Computer and System Sciences 83, 1, 180206.
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.
Gottlob, G., Manna, M. and Pieris, A. 2013. Combining decidability paradigms for existential rules. Theory and Practice of Logic Programming 13, 4–5, 877892.
Gottlob, G., Orsi, G. and Pieris, A. 2014. Query rewriting and optimization for ontological databases. ACM TODS 39, 3, 25:125:46.
Gottlob, G., Pieris, A. and Tendera, L. 2013. Querying the guarded fragment with transitivity. In Proc. of ICALP'13, 287–298.
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.
Krötzsch, M. and Rudolph, S. 2011. Extending decidable existential rules by joining acyclicity and guardedness. In Proc. of IJCAI'11, 963–968.
Leone, N., Manna, M., Terracina, G. and Veltri, P. 2012. Efficiently computable datalog programs. In Proc. of KR'12.
Rosati, R. 2006. On the decidability and finite controllability of query processing in databases with incomplete information. In Proc. of PODS'06.
Rosati, R. 2007. The limits of querying ontologies. In Proc. of ICDT'07, 164–178.
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Theory and Practice of Logic Programming
  • ISSN: 1471-0684
  • EISSN: 1475-3081
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