Existential Rules and Bayesian Networks for Probabilistic Ontological Data Exchange
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Abstract
We investigate the problem of exchanging probabilistic data between ontology-based probabilistic databases. The probabilities of the probabilistic source databases are compactly and flexibly encoded via Bayesian networks, which are closely related to the management of provenance. For the ontologies and the ontology mappings, we consider existential rules from the Datalog+/– family. We analyze the computational complexity of the problem of deciding whether there exists a probabilistic (universal) solution for a given probabilistic source database relative to a (probabilistic) ontological data exchange problem. We provide a host of complexity results for this problem for different classes of existential rules. We also analyze the complexity of answering UCQs (unions of conjunctive queries) in this framework.
Keywords
Bayesian Network Description Logic Conjunctive Query Source Database Query Answering
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References
- 1.Arenas, M., Botoeva, E., Calvanese, D., Ryzhikov, V.: Exchanging OWL2 QL knowledge bases. In: Proc. IJCAI, pp. 703–710 (2013)Google Scholar
- 2.Arenas, M., Botoeva, E., Calvanese, D., Ryzhikov, V., Sherkhonov, E.: Exchanging description logic knowledge bases. In: Proc. KR, pp. 563–567 (2012)Google Scholar
- 3.Arenas, M., Pérez, J., Reutter, J.L.: Data exchange beyond complete data. J. ACM 60(4), 28:1–28:59 (2013)CrossRefGoogle Scholar
- 4.Baader, F.: Least common subsumers and most specific concepts in a description logic with existential restrictions and terminological cycles. In: Proc. IJCAI, pp. 364–369 (2003)Google Scholar
- 5.Baader, F., Brandt, S., Lutz, C.: Pushing the \(\cal EL\) envelope. In: Proc. IJCAI, pp. 364–369 (2005)Google Scholar
- 6.Calì, A., Gottlob, G., Kifer, M.: Taming the infinite chase: Query answering under expressive relational constraints. J. Artif. Intell. Res. 48, 115–174 (2013)zbMATHGoogle Scholar
- 7.Cali, A., Gottlob, G., Lukasiewicz, T., Marnette, B., Pieris, A.: Datalog+/-: a family of logical knowledge representation and query languages for new applications. In: Proc. LICS, pp. 228–242 (2010)Google Scholar
- 8.Calì, A., Gottlob, G., Pieris, A.: Towards more expressive ontology languages: The query answering problem. Artif. Intell. 193, 87–128 (2012)CrossRefzbMATHGoogle Scholar
- 9.Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: The DL-Lite family. J. Autom. Reasoning 39(3), 385–429 (2007)CrossRefzbMATHGoogle Scholar
- 10.Cooper, G.F.: The computational complexity of probabilistic inference using Bayesian belief networks. Artif. Intell. 42(2–3) (1990)Google Scholar
- 11.Fagin, R., Kimelfeld, B., Kolaitis, P.G.: Probabilistic data exchange. J. ACM 58(4), 15:1–15:55 (2011)MathSciNetCrossRefGoogle Scholar
- 12.Fagin, R., Kolaitis, P.G., Miller, R.J., Popa, L.: Data exchange: Semantics and query answering. Theor. Comput. Sci. 336(1), 89–124 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
- 13.Fuhr, N., Rölleke, T.: A probabilistic relational algebra for the integration of information retrieval and database systems. ACM Trans. Inf. Sys. 15(1), 32–66 (1997)CrossRefGoogle Scholar
- 14.Green, T.J., Karvounarakis, G., Tannen, V.: Provenance semirings. In: Proc. PODS, pp. 31–40 (2007)Google Scholar
- 15.Imielinski, T.: Witold Lipski, J.: Incomplete information in relational databases. J. ACM 31(4), 761–791 (1984)MathSciNetCrossRefGoogle Scholar
- 16.Johnson, D.S.: A catalog of complexity classes. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. A, chap. 2, pp. 67–161. MIT Press (1990)Google Scholar
- 17.Krisnadhi, A., Lutz, C.: Data complexity in the \(\cal EL\) family of description logics. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 333–347. Springer, Heidelberg (2007) CrossRefGoogle Scholar
- 18.Lenzerini, M.: Data integration: a theoretical perspective. In: Proc. PODS, pp. 233–246 (2002)Google Scholar
- 19.Lukasiewicz, T., Martinez, M.V., Pieris, A., Simari, G.I.: From classical to consistent query answering under existential rules. In: Proc. AAAI, pp. 1546–1552 (2015)Google Scholar
- 20.Meliou, A., Gatterbauer, W., Suciu, D.: Bringing provenance to its full potential using causal reasoning. In: Proc. TAPP (2011)Google Scholar
- 21.Papadimitriou, C.H.: Computational Complexity. Addison-Wesley (1994)Google Scholar
- 22.Poggi, A., Lembo, D., Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. Data Sem. 10, 133–173 (2008)Google Scholar
- 23.Roth, D.: On the hardness of approximate reasoning. Artif. Intell. 82, 273–302 (1996)CrossRefGoogle Scholar
- 24.Suciu, D., Olteanu, D., Ré, C., Koch, C.: Probabilistic Databases. M & C (2011)Google Scholar
- 25.Vardi, M.Y.: The complexity of relational query languages (extended abstract). In: Proc. STOC, pp. 137–146 (1982)Google Scholar
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