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Well−Founded Semantics for Extended Datalog and Ontological Reasoning

André Hernich‚ Clemens Kupke‚ Thomas Lukasiewicz and Georg Gottlob


The Datalog± family of expressive extensions of Datalog has recently been introduced as a new paradigm for query answering over ontologies, which captures and extends several common description logics. It extends plain Datalog by features such as existentially quantified rule heads and, at the same time, restricts the rule syntax so as to achieve decidability and tractability. In this paper, we continue the research on Datalog±. More precisely, we generalize the well-founded semantics (WFS), as the standard semantics for nonmonotonic normal programs in the database context, to Datalog± programs with negation under the unique name assumption (UNA). We prove that for guarded Datalog± with negation under the standard WFS, answering normal Boolean conjunctive queries is decidable, and we provide precise complexity results for this problem, namely, in particular, completeness for PTIME (resp., 2-EXPTIME) in the data (resp., combined) complexity.

Book Title
Proceedings of the 32nd ACM Symposium on Principles of Database Systems‚ PODS 2013‚ New York‚ New York‚ USA‚ June 22−27‚ 2013
Richard Hull and Wenfei Fan
ACM Press