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Taming the infinite chase: Query answering under expressive relational constraints. (2013)

by A Calı, G Gottlob, M Kifer
Venue:JAIR,
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A general Datalog-based framework for tractable query answering over ontologies

by Andrea Calì, Georg Gottlob, Thomas Lukasiewicz - In Proc. PODS-2009. 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 DL-Lite family of tractable description logics (DLs) [11, 19]. ..."
Abstract - Cited by 135 (24 self) - Add to MetaCart
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 DL-Lite family of tractable description logics (DLs) [11, 19]. An important result of these works is that the main
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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...

Tractable Query Answering and Rewriting under Description Logic Constraints

by Héctor Pérez-urbina, Boris Motik, Ian Horrocks - 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 ..."
Abstract - Cited by 62 (9 self) - Add to MetaCart
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 PTime-complete w.r.t. data complexity. Our algorithm deals with various description logics of the EL and DL-Lite families and is worst-case optimal w.r.t. data complexity for all of them. 1
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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...

Query rewriting and optimization for . . .

by Georg Gottlob, GIORGIO ORSI, ANDREAS PIERIS , 2014
"... ..."
Abstract - Cited by 59 (7 self) - Add to MetaCart
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A Better Uncle For OWL -- Nominal Schemas for Integrating Rules and Ontologies

by Markus Krötzsch, Frederick Maier, Adila A. Krisnadhi, Pascal Hitzler , 2011
"... We propose a description-logic 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 DL-safe rules (as expressible in SWRL or RIF) in their native syntax. We show that adding nominal s ..."
Abstract - Cited by 38 (17 self) - Add to MetaCart
We propose a description-logic 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 DL-safe rules (as expressible in SWRL or RIF) in their native syntax. We show that adding nominal schemas to OWL 2 does not increase the worst-case 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.
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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...

Querying the guarded fragment

by Vince Bárány, Georg Gottlob, Martin Otto - PROCEEDINGS OF THE 25TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, LICS 2010 , 2010
"... Evaluating a Boolean conjunctive query q against a guarded first-order 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 ..."
Abstract - Cited by 38 (12 self) - Add to MetaCart
Evaluating a Boolean conjunctive query q against a guarded first-order 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 finite-model 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 2EXPTIME-complete. We further show the following results: (iii) the existence of polynomial-size conformal covers of arbitrary hypergraphs; (iv) a new proof of the finite model property of the clique-guarded fragment; (v) the small model property of the guarded fragment with optimal bounds; (vi) a polynomial-time solution to the canonisation problem modulo guarded bisimulation, which yields (vii) a capturing result for guarded bisimulation invariant PTIME.
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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....

T.: Datalog ± : a unified approach to ontologies and integrity constraints

by Andrea Calì, Georg Gottlob, Thomas Lukasiewicz, Oxford Ox Qd - 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 ..."
Abstract - Cited by 36 (5 self) - Add to MetaCart
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 DL-Lite family of description logics and F-Logic 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
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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...

Rewriting ontological queries into small nonrecursive datalog programs

by Georg Gottlob, Thomas Schwentick
"... We consider the setting of ontological database access, where an A-box is given in form of a relational database D and where a Boolean conjunctive query q has to be evaluated against D modulo a T-box Σ formulated in DL-Lite or Linear Datalog ±. It is well-known that (Σ, q) can be rewritten into an ..."
Abstract - Cited by 35 (3 self) - Add to MetaCart
We consider the setting of ontological database access, where an A-box is given in form of a relational database D and where a Boolean conjunctive query q has to be evaluated against D modulo a T-box Σ formulated in DL-Lite or Linear Datalog ±. It is well-known 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 DL-Lite 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.
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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...

Walking the Complexity Lines for Generalized Guarded Existential Rules

by Jean-françois Baget, Marie-laure Mugnier, Sebastian Rudolph, Michaël Thomazo - PROCEEDINGS OF THE TWENTY-SECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... We establish complexities of the conjunctive query entailment problem for classes of existential rules (i.e. Tuple-Generating 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 ..."
Abstract - Cited by 33 (9 self) - Add to MetaCart
We establish complexities of the conjunctive query entailment problem for classes of existential rules (i.e. Tuple-Generating 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) frontier-guarded rules. We provide a generic algorithm for query entailment with gbts, which is worst-case 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 frontier-one, frontier-guarded and weakly frontier-guarded rules, with respect to combined complexity (with bounded and unbounded predicate arity) and data complexity.

On Chase Termination Beyond Stratification

by Michael Meier, Michael Schmidt, Georg Lausen
"... 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 ..."
Abstract - Cited by 31 (2 self) - Add to MetaCart
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 so-called T-hierarchy 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 T-hierarchy and accounts for the complexity of termination conditions. As another contribution, we study the problem of data-dependent 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.
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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] ...

Extending decidable existential rules by joining acyclicity and guardedness

by Markus Krötzsch, Sebastian Rudolph - In IJCAI , 2011
"... Existential rules, i.e. Datalog extended with exis-tential quantifiers in rule heads, are currently stud-ied under a variety of names such as Datalog+/–, ∀∃-rules, and tuple-generating dependencies. The renewed interest in this formalism is fuelled by a wealth of recently discovered language frag-me ..."
Abstract - Cited by 30 (7 self) - Add to MetaCart
Existential rules, i.e. Datalog extended with exis-tential quantifiers in rule heads, are currently stud-ied under a variety of names such as Datalog+/–, ∀∃-rules, and tuple-generating dependencies. The renewed interest in this formalism is fuelled by a wealth of recently discovered language frag-ments for which query answering is decidable. This paper extends and consolidates two of the main approaches in this field – acyclicity and guard-edness – by providing (1) complexity-preserving generalisations of weakly acyclic and weakly (frontier-)guarded rules, and (2) a novel formal-ism 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
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