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2016 | OriginalPaper | Buchkapitel

On the Complexity of Evaluating Regular Path Queries over Linear Existential Rules

verfasst von : Meghyn Bienvenu, Michaël Thomazo

Erschienen in: Web Reasoning and Rule Systems

Verlag: Springer International Publishing

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Abstract

In the setting of ontology-mediated query answering, a query is evaluated over a knowledge base consisting of a database instance and an ontology. While most work in the area focuses on conjunctive queries, navigational queries are gaining increasing attention. In this paper, we investigate the complexity of evaluating the standard form of navigational queries, namely two-way regular path queries, over knowledge bases whose ontology is expressed by means of linear existential rules. More specifically, we show how to extend an approach developed for DL-Lite\(_\mathcal {R}\) to obtain an exponential-time decision procedure for linear rules. We prove that this algorithm achieves optimal worst-case complexity by establishing a matching ExpTime lower bound.

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Fußnoten
1
As we only consider the two-way variant, we will use the abbreviation RPQ instead of the more traditional 2RPQ.
 
2
Note that x is required to determine the arity of \(\textit{conf}\).
 
Literatur
1.
Zurück zum Zitat Baget, J., Leclère, M., Mugnier, M., Salvat, E.: Extending decidable cases for rules with existential variables. In: Proceedings of IJCAI, pp. 677–682 (2009) Baget, J., Leclère, M., Mugnier, M., Salvat, E.: Extending decidable cases for rules with existential variables. In: Proceedings of IJCAI, pp. 677–682 (2009)
2.
Zurück zum Zitat Baget, J., Bienvenu, M., Mugnier, M., Rocher, S.: Combining existential rules and transitivity: next steps. In: Proceedings of IJCAI, pp. 2720–2726 (2015) Baget, J., Bienvenu, M., Mugnier, M., Rocher, S.: Combining existential rules and transitivity: next steps. In: Proceedings of IJCAI, pp. 2720–2726 (2015)
3.
Zurück zum Zitat Bienvenu, M., Calvanese, D., Ortiz, M., Šimkus, M.: Nested regular path queries in description logics. In: Proceedings of KR (2014) Bienvenu, M., Calvanese, D., Ortiz, M., Šimkus, M.: Nested regular path queries in description logics. In: Proceedings of KR (2014)
4.
Zurück zum Zitat Bienvenu, M., Ortiz, M.: Ontology-mediated query answering with data-tractable description logics. In: Faber, W., Paschke, A. (eds.) Reasoning Web 2015. LNCS, vol. 9203, pp. 218–307. Springer, Heidelberg (2015)CrossRef Bienvenu, M., Ortiz, M.: Ontology-mediated query answering with data-tractable description logics. In: Faber, W., Paschke, A. (eds.) Reasoning Web 2015. LNCS, vol. 9203, pp. 218–307. Springer, Heidelberg (2015)CrossRef
5.
Zurück zum Zitat Bienvenu, M., Ortiz, M., Simkus, M.: Regular path queries in lightweight description logics: complexity and algorithms. J. Artif. Intell. Res. (JAIR) 53, 315–374 (2015)MathSciNetMATH Bienvenu, M., Ortiz, M., Simkus, M.: Regular path queries in lightweight description logics: complexity and algorithms. J. Artif. Intell. Res. (JAIR) 53, 315–374 (2015)MathSciNetMATH
6.
Zurück zum Zitat Bourhis, P., Krötzsch, M., Rudolph, S.: How to best nest regular path queries. In: Proceedings of DL, pp. 404–415 (2014) Bourhis, P., Krötzsch, M., Rudolph, S.: How to best nest regular path queries. In: Proceedings of DL, pp. 404–415 (2014)
7.
Zurück zum Zitat Calì, A., Gottlob, G., Kifer, M.: Taming the infinite chase: query answering under expressive relational constraints. In: Proceedings of KR, pp. 70–80 (2008) Calì, A., Gottlob, G., Kifer, M.: Taming the infinite chase: query answering under expressive relational constraints. In: Proceedings of KR, pp. 70–80 (2008)
8.
Zurück zum Zitat Calvanese, D., Eiter, T., Ortiz, M.: Answering regular path queries in expressive description logics: an automata-theoretic approach. In: Proceedings of AAAI, pp. 391–396 (2007) Calvanese, D., Eiter, T., Ortiz, M.: Answering regular path queries in expressive description logics: an automata-theoretic approach. In: Proceedings of AAAI, pp. 391–396 (2007)
9.
Zurück zum Zitat Calvanese, D., Eiter, T., Ortiz, M.: Regular path queries in expressive description logics with nominals. In: Proceedings of IJCAI, pp. 714–720 (2009) Calvanese, D., Eiter, T., Ortiz, M.: Regular path queries in expressive description logics with nominals. In: Proceedings of IJCAI, pp. 714–720 (2009)
10.
Zurück zum Zitat Calvanese, D., Eiter, T., Ortiz, M.: Answering regular path queries in expressive description logics via alternating tree-automata. Inf. Comput. 237, 12–55 (2014)MathSciNetCrossRefMATH Calvanese, D., Eiter, T., Ortiz, M.: Answering regular path queries in expressive description logics via alternating tree-automata. Inf. Comput. 237, 12–55 (2014)MathSciNetCrossRefMATH
11.
Zurück zum Zitat Florescu, D., Levy, A., Suciu, D.: Query containment for conjunctive queries with regular expressions. In: Proceedings of PODS (1998) Florescu, D., Levy, A., Suciu, D.: Query containment for conjunctive queries with regular expressions. In: Proceedings of PODS (1998)
12.
13.
Zurück zum Zitat Grau, B.C., Horrocks, I., Krötzsch, M., Kupke, C., Magka, D., Motik, B., Wang, Z.: Acyclicity notions for existential rules and their application to query answering in ontologies. J. Artif. Intell. Res. (JAIR) 47, 741–808 (2013)MathSciNetMATH Grau, B.C., Horrocks, I., Krötzsch, M., Kupke, C., Magka, D., Motik, B., Wang, Z.: Acyclicity notions for existential rules and their application to query answering in ontologies. J. Artif. Intell. Res. (JAIR) 47, 741–808 (2013)MathSciNetMATH
14.
Zurück zum Zitat Johnson, D.S., Klug, A.C.: Testing containment of conjunctive queries under functional and inclusion dependencies. J. Comput. Syst. Sci. 28(1), 167–189 (1984)MathSciNetCrossRefMATH Johnson, D.S., Klug, A.C.: Testing containment of conjunctive queries under functional and inclusion dependencies. J. Comput. Syst. Sci. 28(1), 167–189 (1984)MathSciNetCrossRefMATH
15.
Zurück zum Zitat Kostylev, E.V., Reutter, J.L., Vrgoc, D.: XPath for DL ontologies. In: Proceedings of AAAI (2015) Kostylev, E.V., Reutter, J.L., Vrgoc, D.: XPath for DL ontologies. In: Proceedings of AAAI (2015)
16.
Zurück zum Zitat Maier, D., Mendelzon, A.O., Sagiv, Y.: Testing implications of data dependencies. ACM Trans. Database Syst. 4(4), 455–469 (1979)CrossRef Maier, D., Mendelzon, A.O., Sagiv, Y.: Testing implications of data dependencies. ACM Trans. Database Syst. 4(4), 455–469 (1979)CrossRef
17.
Zurück zum Zitat Marnette, B.: Generalized schema-mappings: from termination to tractability. In: Proceedings of PODS, pp. 13–22 (2009) Marnette, B.: Generalized schema-mappings: from termination to tractability. In: Proceedings of PODS, pp. 13–22 (2009)
18.
Zurück zum Zitat Ortiz, M., Rudolph, S., Šimkus, M.: Query answering in the Horn fragments of the description logics \(\cal {SHOIQ}\) and \(\cal {SROIQ}\). In: Proceedings of IJCAI (2011) Ortiz, M., Rudolph, S., Šimkus, M.: Query answering in the Horn fragments of the description logics \(\cal {SHOIQ}\) and \(\cal {SROIQ}\). In: Proceedings of IJCAI (2011)
19.
Zurück zum Zitat Stefanoni, G., Motik, B., Krötzsch, M., Rudolph, S.: The complexity of answering conjunctive and navigational queries over OWL 2 EL knowledge bases. J. Artif. Intell. Res. (JAIR) 51, 645–705 (2014)MathSciNetMATH Stefanoni, G., Motik, B., Krötzsch, M., Rudolph, S.: The complexity of answering conjunctive and navigational queries over OWL 2 EL knowledge bases. J. Artif. Intell. Res. (JAIR) 51, 645–705 (2014)MathSciNetMATH
Metadaten
Titel
On the Complexity of Evaluating Regular Path Queries over Linear Existential Rules
verfasst von
Meghyn Bienvenu
Michaël Thomazo
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-45276-0_1