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38
A general Datalogbased framework for tractable query answering over ontologies
 In Proc. PODS2009. ACM
, 2009
"... Ontologies play a key role in the Semantic Web [4], data modeling, and information integration [16]. Recent trends in ontological reasoning have shifted from decidability issues to tractability ones, as e.g. reflected by the work on the DLLite family of tractable description logics (DLs) [11, 19]. ..."
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Cited by 135 (24 self)
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Ontologies play a key role in the Semantic Web [4], data modeling, and information integration [16]. Recent trends in ontological reasoning have shifted from decidability issues to tractability ones, as e.g. reflected by the work on the DLLite family of tractable description logics (DLs) [11, 19]. An important result of these works is that the main
Walking the Complexity Lines for Generalized Guarded Existential Rules
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... We establish complexities of the conjunctive query entailment problem for classes of existential rules (i.e. TupleGenerating Dependencies or Datalog+/rules). Our contribution is twofold. First, we introduce the class of greedy bounded treewidth sets (gbts), which covers guarded rules, and their kno ..."
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Cited by 33 (9 self)
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We establish complexities of the conjunctive query entailment problem for classes of existential rules (i.e. TupleGenerating Dependencies or Datalog+/rules). Our contribution is twofold. First, we introduce the class of greedy bounded treewidth sets (gbts), which covers guarded rules, and their known generalizations, namely (weakly) frontierguarded rules. We provide a generic algorithm for query entailment with gbts, which is worstcase optimal for combined complexity with bounded predicate arity, as well as for data complexity. Second, we classify several gbts classes, whose complexity was unknown, namely frontierone, frontierguarded and weakly frontierguarded rules, with respect to combined complexity (with bounded and unbounded predicate arity) and data complexity.
Ontologybased data access: a study through disjunctive datalog, csp, and mmsnp
 IN: PODS
, 2014
"... Ontologybased data access is concerned with querying incomplete data sources in the presence of domainspecific knowledge provided by an ontology. A central notion in this setting is that of an ontologymediated query, which is a database query coupled with an ontology. In this article, we study se ..."
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Cited by 20 (2 self)
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Ontologybased data access is concerned with querying incomplete data sources in the presence of domainspecific knowledge provided by an ontology. A central notion in this setting is that of an ontologymediated query, which is a database query coupled with an ontology. In this article, we study several classes of ontologymediated queries, where the database queries are given as some form of conjunctive query and the ontologies are formulated in description logics or other relevant fragments of firstorder logic, such as the guarded fragment and the unary negation fragment. The contributions of the article are threefold. First, we show that popular ontologymediated query languages have the same expressive power as natural fragments of disjunctive datalog, and we study the relative succinctness of ontologymediated queries and disjunctive datalog queries. Second, we establish intimate connections between ontologymediated queries and constraint satisfaction problems (CSPs) and their logical generalization, MMSNP formulas. Third, we exploit these connections to obtain new results regarding: (i) firstorder rewritability and datalog rewritability of ontologymediated queries; (ii) P/NP dichotomies for ontologymediated queries; and (iii) the query containment problem for ontologymediated queries.
Guarded negation
"... Abstract. We consider restrictions of firstorder logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP, extend the guarded fragment of firstorder logic and guard ..."
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Abstract. We consider restrictions of firstorder logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP, extend the guarded fragment of firstorder logic and guarded least fixpoint logic, respectively. They also extend the recently introduced unary negation fragments of firstorder logic and of least fixpoint logic. We show that the satisfiability problem for GNFO and for GNFP is 2ExpTimecomplete, both on arbitrary structures and on finite structures. We also study the complexity of the associated model checking problems. Finally, we show that GNFO and GNFP are not only computationally well behaved, but also model theoretically: we show that GNFO and GNFP have the treelike model property and that GNFO has the finite model property, and we characterize the expressive power of GNFO in terms of invariance for an appropriate notion of bisimulation. 1
Highly acyclic groups, hypergraph covers and the guarded fragment
 JOURNAL OF THE ACM
"... We construct finite groups whose Cayley graphs have large girth even w.r.t. a discounted distance measure that contracts arbitrarily long sequences of edges from the same colour class (subgroup), and only counts transitions between colour classes (cosets). These groups are shown to be useful in the ..."
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Cited by 14 (8 self)
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We construct finite groups whose Cayley graphs have large girth even w.r.t. a discounted distance measure that contracts arbitrarily long sequences of edges from the same colour class (subgroup), and only counts transitions between colour classes (cosets). These groups are shown to be useful in the construction of finite bisimilar hypergraph covers that avoid any small cyclic configurations. We present two applications to the finite model theory of the guarded fragment: a strengthening of the known finite model property for GF and the characterisation of GF as the guarded bisimulation invariant fragment of firstorder logic in the sense of finite model theory.
Unary negation
, 2011
"... We study fragments of firstorder logic and of least fixed point logic that allow only unary negation: negation of formulas with at most one free variable. These logics generalize many interesting known formalisms, including modal logic and the µcalculus, as well as conjunctive queries and monadic ..."
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Cited by 12 (4 self)
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We study fragments of firstorder logic and of least fixed point logic that allow only unary negation: negation of formulas with at most one free variable. These logics generalize many interesting known formalisms, including modal logic and the µcalculus, as well as conjunctive queries and monadic Datalog. We show that satisfiability and finite satisfiability are decidable for both fragments, and we pinpoint the complexity of satisfiability, finite satisfiability, and model checking. We also show that the unary negation fragment of firstorder logic is modeltheoretically very well behaved. In particular, it enjoys Craig interpolation and the Beth property.
Disjunctive datalog with existential quantifiers: Semantics, decidability, and complexity issues. Theory and Practice of Logic Programming
, 2012
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Efficient Approximations of Conjunctive Queries
"... When finding exact answers to a query over a large database is infeasible, it is natural to approximate the query by a more efficient one that comes from a class with good bounds on the complexity of query evaluation. In this paper we study such approximations for conjunctive queries. These queries ..."
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Cited by 6 (4 self)
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When finding exact answers to a query over a large database is infeasible, it is natural to approximate the query by a more efficient one that comes from a class with good bounds on the complexity of query evaluation. In this paper we study such approximations for conjunctive queries. These queries are of special importance in databases, and we have a very good understanding of the classes that admit fast query evaluation, such as acyclic, or bounded (hyper)treewidth queries. We define approximations of a given query Q as queries from one of those classes that disagree with Q as little as possible. We mostly concentrate on approximations that are guaranteed to return correct answers. We prove that for the above classes of tractable conjunctive queries, approximations always exist, and are at most polynomial in the size of the original query. This follows from general results we establish that relate closure properties of classes of conjunctive queries to the existence of approximations. We also show that in many cases, the size of approximations is bounded by the size of the query they approximate. We establish a number of results showing how combinatorial properties of queries affect properties of their approximations, study bounds on the number of approximations, as well as the complexity of finding and identifying approximations. We also look at approximations that return all correct answers and study their properties.
The Impact of Disjunction on Query Answering Under Guardedbased Existential Rules
"... Abstract. We give the complete picture of the complexity of conjunctive query answering under (weakly)(frontier)guarded disjunctive existential rules, i.e., existential rules extended with disjunction, and their main subclasses, linear rules and inclusion dependencies. 1 ..."
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Cited by 6 (3 self)
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Abstract. We give the complete picture of the complexity of conjunctive query answering under (weakly)(frontier)guarded disjunctive existential rules, i.e., existential rules extended with disjunction, and their main subclasses, linear rules and inclusion dependencies. 1
EqualityFriendly WellFounded Semantics and Applications to Description Logics
"... We tackle the problem of defining a wellfounded semantics for Datalog rules with existentially quantified variables in their heads and negations in their bodies. In particular, we provide a wellfounded semantics (WFS) for the recent Datalog ± family of ontology languages, which covers several impo ..."
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Cited by 5 (2 self)
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We tackle the problem of defining a wellfounded semantics for Datalog rules with existentially quantified variables in their heads and negations in their bodies. In particular, we provide a wellfounded semantics (WFS) for the recent Datalog ± family of ontology languages, which covers several important description logics (DLs). To do so, we generalize Datalog ± by nonstratified nonmonotonic negation in rule bodies, and we define a WFS for this generalization via guarded fixedpoint logic. We refer to this approach as equalityfriendly WFS, since it has the advantage that it does not make the unique name assumption (UNA); this brings it close to OWL and its profiles as well as typical DLs, which also do not make the UNA. We prove that for guarded Datalog ± with negation under the equalityfriendly WFS, conjunctive query answering is decidable, and we provide precise complexity results for this problem. From these results, we obtain precise definitions of the standard WFS extensions of EL and of members of the DLLite family, as well as corresponding complexity results for query answering.