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133
A Novel Combination of Answer Set Programming with Description Logics for the Semantic Web
 IN PROC. KR2004
, 2004
"... Abstract. We present a novel combination of disjunctive logic programs under the answer set semantics with description logics for the Semantic Web. The combination is based on a wellbalanced interface between disjunctive logic programs and description logics, which guarantees the decidability of th ..."
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Cited by 282 (59 self)
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Abstract. We present a novel combination of disjunctive logic programs under the answer set semantics with description logics for the Semantic Web. The combination is based on a wellbalanced interface between disjunctive logic programs and description logics, which guarantees the decidability of the resulting formalism without assuming syntactic restrictions. We show that the new formalism has very nice semantic properties. In particular, it faithfully extends both disjunctive programs and description logics. Furthermore, we describe algorithms for reasoning in the new formalism, and we give a precise picture of its computational complexity. We also provide a special case with polynomial data complexity. 1
Data complexity of query answering in description logics
 IN PROC. OF KR 2006
, 2006
"... In this paper we study data complexity of answering conjunctive queries over Description Logic knowledge bases constituted by an ABox and a TBox. In particular, we are interested in characterizing the FOLreducibility and the polynomial tractability boundaries of conjunctive query answering, dependi ..."
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Cited by 210 (75 self)
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In this paper we study data complexity of answering conjunctive queries over Description Logic knowledge bases constituted by an ABox and a TBox. In particular, we are interested in characterizing the FOLreducibility and the polynomial tractability boundaries of conjunctive query answering, depending on the expressive power of the Description Logic used to specify the knowledge base. FOLreducibility means that query answering can be reduced to evaluating queries over the database corresponding to the ABox. Since firstorder queries can be expressed in SQL, the importance of FOLreducibility is that, when query answering enjoys this property, we can take advantage of Data Base Management System (DBMS) techniques for both representing data, i.e., ABox assertions, and answering queries via reformulation into SQL. What emerges from our complexity analysis is that the Description Logics of the DLLite family are the maximal logics allowing conjunctive query answering through standard database technology. In this sense, they are the first Description Logics specifically tailored for effective query answering over very large ABoxes.
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 (10 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 37 (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 36 (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.
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 (2 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.
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 35 (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
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 (10 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.
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 31 (8 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
The Consistency Extractor System: Answer Set Programs for Consistent Query Answering in Databases
, 2010
"... We describe the Consistency Extractor System (ConsEx) that computes consistent answers to Datalog queries with negation posed to relational databases that may be inconsistent with respect to certain integrity constraints. In order to solve this task, ConsEx uses answers set programming. More precise ..."
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Cited by 17 (9 self)
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We describe the Consistency Extractor System (ConsEx) that computes consistent answers to Datalog queries with negation posed to relational databases that may be inconsistent with respect to certain integrity constraints. In order to solve this task, ConsEx uses answers set programming. More precisely, ConsEx uses disjunctive logic programs with stable models semantics to specify and reason with the repairs, i.e. with the consistent virtual instances that minimally depart from the original database. The consistent information is invariant under all repairs. ConsEx achieves efficient query evaluation by implementing magic sets techniques. We describe the general methodology, its optimizations for query answering, and the architecture of the system. We also present encouraging experimental results.