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...s been an open problem to date, since it is in general based on several strata of infinite models. Related Work. The results of the present paper are related to but very different from the results in =-=[6]-=-, where complexity issues of GTGDs as well as of another class, called weakly guarded TGDs, were first studied. There, it was shown that the combined complexity of query answering and fact inference w...

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...consider constraints tailored to express entity-relationship schemas; Fuxman and Miller [18] consider key constraints expressed over potentially inconsistent databases; and very recently, Calì et al. =-=[7, 8]-=- proposed a general datalog-based framework for query answering in which constraints are expressed as restricted TGDs (tuple-generating dependencies) and EGDs (equality-generating dependencies) [1]. D...

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...digm has attracted much interest recently, and has been studied under a variety of names such as Datalog+/–, ∀∃-rules, and – primarily in the database community – tuple-generating dependencies (TGDs) =-=[2, 3, 6, 7, 8, 9, 13, 14]-=-. As in the combination of rules and DL, reasoning with existential rules is undecidable without further restrictions. A chief interest of many of the above works thus is to establish formalisms for w...

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... and naturally extend propositional modal logics within first-order logic [1], it has various applications and was more recently shown to be relevant to description logics [15] and to database theory =-=[42, 7]-=-. Fragments of GF were recently studied for query answering in such contexts, see e.g. [7, 9, 8, 42, 10, 6, 38]. The main problems studied in the present paper are motivated by such applications. 1.1....

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... of TGDs can be transformed into a set Σ ′ in normal form of size at most quadratic in |Σ|, such that Σ and Σ ′ are equivalent with respect to query answering. The normal form transformation shown in =-=[4]-=- can be achieved in logarithmic space. It is, moreover, easy to see that this very simple transformation preserves the polynomial witness property. For a database D for R, and a set of tgds Σ on R, th...

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...aboratory, University of Oxford, UK firstname.lastname@comlab.ox.ac.uk 2 Oxford-Man Institute of Quantitative Finance, University of Oxford, UK In this talk, we survey the results of two recent works =-=[1, 2]-=- on a family of expressive extensions of Datalog, called Datalog ± , towards query answering over ontologies. Ontologies are fundamental to the Semantic Web. They also proved to be useful, due to thei...

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...alism in the following section, and show how it can be used to exclude unintended infinite models such as the one in Figure 3. Our formalism is related to weakly guarded tuple generating dependencies =-=[9]-=- and the guarded fragment of first-order logic [2], which allow for axiomatizing nontree structures of bounded treewidth. Unlike these formalisms, however, graph-extended knowledge bases allow for fun...

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... presence of constraints, with a focus on scenarios where the chase with the given constraint set does not necessarily terminate. This problem was first considered in [13] and recently generalized in =-=[5, 6]-=-. A key idea in [5] is an overestimation of the set of positions in which null values might occur, using the concept of so-called affected positions. In particular, affected positions are used in [5] ...