Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-16T09:19:47.129Z Has data issue: false hasContentIssue false
  • English
  • Français

Disjunctive datalog with existential quantifiers: Semantics, decidability, and complexity issues

Published online by Cambridge University Press:  05 September 2012

MARIO ALVIANO ,
WOLFGANG FABER ,
NICOLA LEONE  and
MARCO MANNA
MARIO ALVIANO
Affiliation:
Department of Mathematics, University of Calabria, Italy (e-mail: [email protected], [email protected], [email protected], [email protected])
WOLFGANG FABER
Affiliation:
Department of Mathematics, University of Calabria, Italy (e-mail: [email protected], [email protected], [email protected], [email protected])
NICOLA LEONE
Affiliation:
Department of Mathematics, University of Calabria, Italy (e-mail: [email protected], [email protected], [email protected], [email protected])
MARCO MANNA
Affiliation:
Department of Mathematics, University of Calabria, Italy (e-mail: [email protected], [email protected], [email protected], [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic language. Disjunctive Datalog is useful in a wide range of applications, ranging from Databases (e.g., Data Integration) to Artificial Intelligence (e.g., diagnosis and planning under incomplete knowledge). However, in recent years an important shortcoming of Datalog-based languages became evident, e.g. in the context of data-integration (consistent query-answering, ontology-based data access) and Semantic Web applications: The language does not permit any generation of and reasoning with unnamed individuals in an obvious way. In general, it is weak in supporting many cases of existential quantification. To overcome this problem, Datalog∃ has recently been proposed, which extends traditional Datalog by existential quantification in rule heads. In this work, we propose a natural extension of Disjunctive Datalog and Datalog∃, called Datalog∃,˅, which allows both disjunctions and existential quantification in rule heads and is therefore an attractive language for knowledge representation and reasoning, especially in domains where ontology-based reasoning is needed. We formally define syntax and semantics of the language Datalog∃,˅, and provide a notion of instantiation, which we prove to be adequate for Datalog∃,˅. A main issue of Datalog∃ and hence also of Datalog∃,˅ is that decidability is no longer guaranteed for typical reasoning tasks. In order to address this issue, we identify many decidable fragments of the language, which extend, in a natural way, analog classes defined in the non-disjunctive case. Moreover, we carry out an in-depth complexity analysis, deriving interesting results which range from Logarithmic Space to Exponential Time.

Keywords

datalognon-monotonic reasoningdecidabilitycomplexity
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 12 , Issue 4-5: 28th International Conference on Logic Programming , July 2012 , pp. 701 - 718
Copyright
Copyright © Cambridge University Press 2012

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.)

References

Andréka, H., Németi, I. and VanBenthem, J. Benthem, J. 1998. Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic 27, 217–274.CrossRefGoogle Scholar
Barany, V., Gottlob, G. and Otto, M. 2010. Querying the guarded fragment. In Proceedings of the 25th Annual IEEE Symposium on LICS. 1–10.CrossRefGoogle Scholar
Calì, A., Gottlob, G. and Kifer, M. 2008. Taming the infinite chase: Query answering under expressive relational constraints. In Proceedings of the 11th KR International Conference. 70–80. Revised version: http://dbai.tuwien.ac.at/staff/gottlob/CGK.pdf.Google Scholar
Calì, A., Gottlob, G. and Lukasiewicz, T. 2009. A general datalog-based framework for tractable query answering over ontologies. In Proceedings of the 28th PODS Symposium. 77–86.Google Scholar
Calì, A., Gottlob, G. and Pieris, A. 2010a. Advanced processing for ontological queries. PVLDB 3, 1, 554–565.Google Scholar
Calì, A., Gottlob, G. and Pieris, A. 2010b. Query answering under non-guarded rules in Datalog±. In Proceedings of the 4th RR International Conferences, vol. 6333. 1–17.Google Scholar
Calì, A., Gottlob, G. and Pieris, A. 2011. New expressive languages for ontological query answering. In Proceedings of the 25th AAAI Conference on AI. 1541–1546.CrossRefGoogle Scholar
Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Poggi, A., Rodriguez-Muro, M. and Rosati, R. 2009. Ontologies and databases: The DL-Lite approach. In Reasoning Web. LNCS, vol. 5689. Springer, 255–356.Google Scholar
Calvanese, D., Giacomo, G., Lembo, D., Lenzerini, M. and Rosati, R. 2007. Tractable reasoning and efficient query answering in description logics: The DL-Lite family. Journal of Automatic Reasoning 39, 385–429.CrossRefGoogle Scholar
Chekuri, C. and Rajaraman, A. 2000. Conjunctive query containment revisited. Theoretical Computer Science 239, 2, 211–229.CrossRefGoogle Scholar
De Moor, O., Gottlob, G., Furche, T. and Sellers, A., Eds. 2011. Datalog Reloaded. First International Workshop, Datalog 2010. Revised Selected Papers. LNCS, vol. 6702. Springer Verlag.Google Scholar
Deutsch, A., Nash, A. and Remmel, J. 2008. The chase revisited. In Proceedings of the 27th PODS Symposium 149–158.CrossRefGoogle Scholar
Eiter, T., Faber, W., Leone, N., Pfeifer, G. and Polleres, A. 2004. A logic programming approach to knowledge-state planning: Semantics and complexity. ACM TOCL 5, 2, 206–263.CrossRefGoogle Scholar
Eiter, T., Gottlob, G. and Mannila, H. 1997. Disjunctive datalog. ACM TODS 22, 3, 364–418.CrossRefGoogle Scholar
Fagin, R., Kolaitis, P. G., Miller, R. J. and Popa, L. 2005. Data exchange: Semantics and query answering. TCS 336, 1, 89–124.CrossRefGoogle Scholar
Ferraris, P., Lee, J. and Lifschitz, V. 2011. Stable models and circumscription. Artificial Intelligence 175, 1, 236–263.CrossRefGoogle Scholar
Gottlob, G., Leone, N. and Scarcello, F. 1999. Hypertree decompositions and tractable queries. In Proceedings of the 18th PODS Symp. 21–32.CrossRefGoogle Scholar
Grädel, E. 1999. On the restraining power of guards. The Journal of Symbolic Logic 64, 4, 1719–1742.CrossRefGoogle Scholar
Greco, S., Spezzano, F. and Trubitsyna, I. 2011. Stratification criteria and rewriting techniques for checking chase termination. PVLDB 4, 11, 1158–1168.Google Scholar
Hustadt, U., Motik, B. and Sattler, U. 2004. Reducing SHIQ- Descrption logic to disjunctive datalog programs. In Proceedings of the 9th KR International Conference. 152–162.Google Scholar
Johnson, D. and Klug, A. 1984. Testing containment of conjunctive queries under functional and inclusion dependencies. Journal of Computer and System Sciences 28, 1, 167–189.CrossRefGoogle Scholar
Kollia, I., Glimm, B. and Horrocks, I. 2011. SPARQL query answering over OWL ontologies. In Proceedings of the 24th DL International Workshop. LNCS, vol. 6643. Springer, 382–396.Google Scholar
Leone, N., Gottlob, G., Rosati, R., Eiter, T., Faber, W., Fink, M., Greco, G., Ianni, G., Kałka, E., Lembo, D., Lenzerini, M., Lio, V., Nowicki, B., Ruzzi, M., Staniszkis, W. and Terracina, G. 2005. The INFOMIX system for advanced integration of incomplete and inconsistent data. In Proceedings of the 24th ACM SIGMOD International Conference on Management of Data. 915–917.CrossRefGoogle Scholar
Leone, N., Manna, M., Terracina, G. and Veltri, P. 2012. Efficiently computable datalog∃ programs. In Proceedings of the 13th KR International Conference, Forthcoming. Long version: www.mat.unical.it/kr2012/shy.pdf.Google Scholar
Maier, D., Mendelzon, A. O. and Sagiv, Y. 1979. Testing implications of data dependencies. ACM TODS 4, 4, 455–469.CrossRefGoogle Scholar
Marnette, B. 2009. Generalized schema-mappings: from termination to tractability. In Proceedings of the 28th PODS Symposium. 13–22.CrossRefGoogle Scholar
Meier, M., Schmidt, M. and Lausen, G. 2009. On chase termination beyond stratification. PVLDB 2, 1, 970–981.Google Scholar
Mugnier, M.-L. 2011. Ontological query answering with existential rules. In Proceedings of the 5th RR International Conference. 2–23.CrossRefGoogle Scholar