Introduction
We consider rules that allow to assert the existence of new individuals, an ability called value invention in databases [AHV95]. These rules are of the form body → head, where the body and the head are function-free conjunctions of atoms, and variables that occur only in the head are existentially quantified, hence their name ∀ ∃-rules in [BLMS09, BLM10] or existential rules in [BMRT11, KR11]. Existential rules have long been studied in databases as high-level constraints called tuple generating dependencies (TGDs) [BV84]. Recently, there has been renewed interest for these rules in the context of ontology-based data access (OBDA), a new paradigm that seeks to exploit the semantics encoded in ontologies while querying data. The deductive database language Datalog could be seen as a natural candidate for expressing ontological knowledge in this context, however its limitation is that it does not allow for value invention, since all variables in a rule head necessarily occur in the rule body. Value invention has been recognized as a necessary prerequisite in an open-world perspective, where all individuals are not known a priori. It is in particular a feature of description logics (DLs), well-known languages dedicated to ontological representation and reasoning. This prerequisite motivated the recent extension of Datalog to existential rules, which gave rise to the Datalog +/- formalism [CGK08, CGL09].
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Mugnier, ML. (2012). Existential Rules: A Graph-Based View. In: Barceló, P., Pichler, R. (eds) Datalog in Academia and Industry. Datalog 2.0 2012. Lecture Notes in Computer Science, vol 7494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32925-8_3
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