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



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.



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Andréka, H., Németi, I. and VanBenthem, J. Benthem, J. 1998. Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic 27, 217274.
Barany, V., Gottlob, G. and Otto, M. 2010. Querying the guarded fragment. In Proceedings of the 25th Annual IEEE Symposium on LICS. 110.
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:
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. 7786.
Calì, A., Gottlob, G. and Pieris, A. 2010a. Advanced processing for ontological queries. PVLDB 3, 1, 554565.
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. 117.
Calì, A., Gottlob, G. and Pieris, A. 2011. New expressive languages for ontological query answering. In Proceedings of the 25th AAAI Conference on AI. 15411546.
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, 255356.
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, 385429.
Chekuri, C. and Rajaraman, A. 2000. Conjunctive query containment revisited. Theoretical Computer Science 239, 2, 211229.
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.
Deutsch, A., Nash, A. and Remmel, J. 2008. The chase revisited. In Proceedings of the 27th PODS Symposium 149158.
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, 206263.
Eiter, T., Gottlob, G. and Mannila, H. 1997. Disjunctive datalog. ACM TODS 22, 3, 364418.
Fagin, R., Kolaitis, P. G., Miller, R. J. and Popa, L. 2005. Data exchange: Semantics and query answering. TCS 336, 1, 89124.
Ferraris, P., Lee, J. and Lifschitz, V. 2011. Stable models and circumscription. Artificial Intelligence 175, 1, 236263.
Gottlob, G., Leone, N. and Scarcello, F. 1999. Hypertree decompositions and tractable queries. In Proceedings of the 18th PODS Symp. 2132.
Grädel, E. 1999. On the restraining power of guards. The Journal of Symbolic Logic 64, 4, 17191742.
Greco, S., Spezzano, F. and Trubitsyna, I. 2011. Stratification criteria and rewriting techniques for checking chase termination. PVLDB 4, 11, 11581168.
Hustadt, U., Motik, B. and Sattler, U. 2004. Reducing SHIQ- Descrption logic to disjunctive datalog programs. In Proceedings of the 9th KR International Conference. 152162.
Johnson, D. and Klug, A. 1984. Testing containment of conjunctive queries under functional and inclusion dependencies. Journal of Computer and System Sciences 28, 1, 167189.
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, 382396.
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. 915917.
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:
Maier, D., Mendelzon, A. O. and Sagiv, Y. 1979. Testing implications of data dependencies. ACM TODS 4, 4, 455469.
Marnette, B. 2009. Generalized schema-mappings: from termination to tractability. In Proceedings of the 28th PODS Symposium. 1322.
Meier, M., Schmidt, M. and Lausen, G. 2009. On chase termination beyond stratification. PVLDB 2, 1, 970981.
Mugnier, M.-L. 2011. Ontological query answering with existential rules. In Proceedings of the 5th RR International Conference. 223.



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