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104
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
Tractable Query Answering and Rewriting under Description Logic Constraints
 Journal of Applied Logic
"... Abstract. Answering queries over an incomplete database w.r.t. a set of constraints is an important computational task with applications in fields as diverse as information integration and metadata management in the Semantic Web. Description Logics (DL) are constraint languages that have been extens ..."
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Cited by 62 (9 self)
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Abstract. Answering queries over an incomplete database w.r.t. a set of constraints is an important computational task with applications in fields as diverse as information integration and metadata management in the Semantic Web. Description Logics (DL) are constraint languages that have been extensively studied in the past with the goal of providing useful modeling constructs while keeping the query answering problem decidable. For many DLs, query answering under constraints can be reduced to query rewriting: given a conjunctive query Q and a set of DL constraints T, the query Q can be transformed into a datalog query QT that takes into account the semantic consequences of T; then, to obtain answers to Q w.r.t. T and some (arbitrary) database instance A, one can simply evaluate QT over A using existing (deductive) database technology, without taking T into account. In this paper, we present a novel query rewriting algorithm that handles constraints modeled in the DL ELHIO ¬ and use it to show that answering conjunctive queries in this setting is PTimecomplete w.r.t. data complexity. Our algorithm deals with various description logics of the EL and DLLite families and is worstcase optimal w.r.t. data complexity for all of them. 1
A Better Uncle For OWL  Nominal Schemas for Integrating Rules and Ontologies
, 2011
"... We propose a descriptionlogic style extension of OWL 2 with nominal schemas which can be used like “variable nominal classes”within axioms. This feature allows ontology languages to express arbitrary DLsafe rules (as expressible in SWRL or RIF) in their native syntax. We show that adding nominal s ..."
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Cited by 38 (17 self)
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We propose a descriptionlogic style extension of OWL 2 with nominal schemas which can be used like “variable nominal classes”within axioms. This feature allows ontology languages to express arbitrary DLsafe rules (as expressible in SWRL or RIF) in their native syntax. We show that adding nominal schemas to OWL 2 does not increase the worstcase reasoning complexity, and we identify a novel tractable language SROELV 3(⊓, ×) that is versatile enough to capture the lightweight languages OWL EL and OWL RL.
Querying the guarded fragment
 PROCEEDINGS OF THE 25TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, LICS 2010
, 2010
"... Evaluating a Boolean conjunctive query q against a guarded firstorder theory ϕ is equivalent to checking whether ϕ ∧ ¬q is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since q may not be guarded, well known results about the decidability, complexity ..."
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Cited by 38 (12 self)
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Evaluating a Boolean conjunctive query q against a guarded firstorder theory ϕ is equivalent to checking whether ϕ ∧ ¬q is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since q may not be guarded, well known results about the decidability, complexity, and finitemodel property of the guarded fragment do not obviously carry over to conjunctive query answering over guarded theories, and had been left open in general. By investigating finite guarded bisimilar covers of hypergraphs and relational structures, and by substantially generalising Rosati’s finite chase, we prove for guarded theories ϕ and (unions of) conjunctive queries q that (i) ϕ  = q iff ϕ =fin q, that is, iff q is true in each finite model of ϕ and (ii) determining whether ϕ  = q is 2EXPTIMEcomplete. We further show the following results: (iii) the existence of polynomialsize conformal covers of arbitrary hypergraphs; (iv) a new proof of the finite model property of the cliqueguarded fragment; (v) the small model property of the guarded fragment with optimal bounds; (vi) a polynomialtime solution to the canonisation problem modulo guarded bisimulation, which yields (vii) a capturing result for guarded bisimulation invariant PTIME.
T.: Datalog ± : a unified approach to ontologies and integrity constraints
 In: Proceedings of the 12th International Conference on Database Theory
, 2009
"... We report on a recently introduced family of expressive extensions of Datalog, called Datalog ± , which is a new framework for representing ontological axioms in form of integrity constraints, and for query answering under such constraints. Datalog ± is derived from Datalog by allowing existentially ..."
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Cited by 36 (5 self)
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We report on a recently introduced family of expressive extensions of Datalog, called Datalog ± , which is a new framework for representing ontological axioms in form of integrity constraints, and for query answering under such constraints. Datalog ± is derived from Datalog by allowing existentially quantified variables in rule heads, and by enforcing suitable properties in rule bodies, to ensure decidable and efficient query answering. We first present different languages in the Datalog ± family, providing tight complexity bounds for all cases but one (where we have a low complexity ac0 upper bound). We then show that such languages are general enough to capture the most common tractable ontology languages. In particular, we show that the DLLite family of description logics and FLogic Lite are expressible in Datalog ±. We finally show how stratified negation can be added to Datalog ± while keeping ontology querying tractable in the data complexity. Datalog ± is a natural and very general framework that can be successfully employed in different contexts such as data integration and exchange. This survey mainly summarizes two recent papers. Categories and Subject Descriptors
Rewriting ontological queries into small nonrecursive datalog programs
"... We consider the setting of ontological database access, where an Abox is given in form of a relational database D and where a Boolean conjunctive query q has to be evaluated against D modulo a Tbox Σ formulated in DLLite or Linear Datalog ±. It is wellknown that (Σ, q) can be rewritten into an ..."
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Cited by 35 (3 self)
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We consider the setting of ontological database access, where an Abox is given in form of a relational database D and where a Boolean conjunctive query q has to be evaluated against D modulo a Tbox Σ formulated in DLLite or Linear Datalog ±. It is wellknown that (Σ, q) can be rewritten into an equivalent nonrecursive Datalog program P that can be directly evaluated over D. However, for Linear Datalog ± or for DLLite versions that allow for role inclusion, the rewriting methods described so far result in a nonrecursive Datalog program P of size exponential in the joint size of Σ and q. This gives rise to the interesting question of whether such a rewriting necessarily needs to be of exponential size. In this paper we show that it is actually possible to translate (Σ, q) into a polynomially sized equivalent nonrecursive Datalog program P.
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.
On Chase Termination Beyond Stratification
"... We study the termination problem of the chase algorithm, a central tool in various database problems such as the constraint implication problem, Conjunctive Query optimization, rewriting queries using views, data exchange, and data integration. The basic idea of the chase is, given a database instan ..."
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Cited by 31 (2 self)
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We study the termination problem of the chase algorithm, a central tool in various database problems such as the constraint implication problem, Conjunctive Query optimization, rewriting queries using views, data exchange, and data integration. The basic idea of the chase is, given a database instance and a set of constraints as input, to fix constraint violations in the database instance. It is wellknown that, for an arbitrary set of constraints, the chase does not necessarily terminate (in general, it is even undecidable if it does or not). Addressing this issue, we review the limitations of existing sufficient termination conditions for the chase and develop new techniques that allow us to establish weaker sufficient conditions. In particular, we introduce two novel termination conditions called safety and inductive restriction, and use them to define the socalled Thierarchy of termination conditions. We then study the interrelations of our termination conditions with previous conditions and the complexity of checking our conditions. This analysis leads to an algorithm that checks membership in a level of the Thierarchy and accounts for the complexity of termination conditions. As another contribution, we study the problem of datadependent chase termination and present sufficient termination conditions w.r.t. fixed instances. They might guarantee termination although the chase does not terminate in the general case. As an application of our techniques beyond those already mentioned, we transfer our results into the field of query answering over knowledge bases where the chase on the underlying database may not terminate, making existing algorithms applicable to broader classes of constraints. 1.
Extending decidable existential rules by joining acyclicity and guardedness
 In IJCAI
, 2011
"... Existential rules, i.e. Datalog extended with existential quantifiers in rule heads, are currently studied under a variety of names such as Datalog+/–, ∀∃rules, and tuplegenerating dependencies. The renewed interest in this formalism is fuelled by a wealth of recently discovered language fragme ..."
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Cited by 30 (7 self)
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Existential rules, i.e. Datalog extended with existential quantifiers in rule heads, are currently studied under a variety of names such as Datalog+/–, ∀∃rules, and tuplegenerating dependencies. The renewed interest in this formalism is fuelled by a wealth of recently discovered language fragments for which query answering is decidable. This paper extends and consolidates two of the main approaches in this field – acyclicity and guardedness – by providing (1) complexitypreserving generalisations of weakly acyclic and weakly (frontier)guarded rules, and (2) a novel formalism of glut(frontier)guarded rules that subsumes both. This builds on an insight that acyclicity can be used to extend any existential rule language while retaining decidability. Besides decidability, combined query complexities are established in all cases. 1