We study the enumeration of answers to ontology-mediated queries (OMQs) where the ontology is a set of guarded TGDs or formulated in the description logic ELI and the query is a conjunctive query (CQ). In addition to the traditional notion of an answer, we propose and study two novel notions of partial answers that can take into account nulls generated by existential quantifiers in the ontology. Our main result is that enumeration of the traditional complete answers and of both kinds of partial answers is possible with linear-time preprocessing and constant delay for OMQs that are both acyclic and free-connex acyclic. We also provide partially matching lower bounds. Similar results are obtained for the related problems of testing a single answer in linear time and of testing multiple answers in constant time after linear time preprocessing. In both cases, the border between tractability and intractability is characterized by similar, but slightly different acyclicity properties.
CNRS（法国国家科学研究中心）；Université Paris Sud（巴黎南大学）；UC Santa Cruz（加州大学圣克鲁兹分校）；University of Bremen（不来梅大学）；University of Liverpool（利物浦大学）
Ontology-based data access is concerned with querying incomplete data sources in the presence of domain-specific knowledge provided by an ontology. A central notion in this setting is that of an ontology-mediated query, which is a database query coupled with an ontology. In this paper, we study several classes of ontology-mediated 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 first-order logic, such as the guarded fragment and the unary-negation fragment. The contributions o…
We consider ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and (unions) of conjunctive queries, studying the rewritability into OMQs based on instance queries (IQs). Our results include exact characterizations of when such a rewriting is possible and tight complexity bounds for deciding rewritability. We also give a tight complexity bound for the related problem of deciding whether a given MMSNP sentence is equivalent to a CSP.
Leipzig University（莱比锡大学）；University of Bremen（不来梅大学）
We study the evaluation of ontology-mediated queries (OMQs) on databases of bounded cliquewidth from the viewpoint of parameterized complexity theory. As the ontology language, we consider the description logics $\mathcal{ALC}$ and $\mathcal{ALCI}$ as well as the guarded two-variable fragment GF$_2$ of first-order logic. Queries are atomic queries (AQs), conjunctive queries (CQs), and unions of CQs. All studied OMQ problems are fixed-parameter linear (FPL) when the parameter is the size of the OMQ plus the cliquewidth. Our main contribution is a detailed analysis of the dependence of the runni…
University of Bremen（不来梅大学）；University of Liverpool（利物浦大学）
We introduce and study several notions of approximation for ontology-mediated queries based on the description logics ALC and ALCI. Our approximations are of two kinds: we may (1) replace the ontology with one formulated in a tractable ontology language such as ELI or certain TGDs and (2) replace the database with one from a tractable class such as the class of databases whose treewidth is bounded by a constant. We determine the computational complexity and the relative completeness of the resulting approximations. (Almost) all of them reduce the data complexity from coNP-complete to PTime, in…
In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology, which can be formulated in a description logic (DL) or using existential rules. In the literature, there exists a multitude of complex techniques for incorporating ontological knowledge into queries. However, few of these approaches were designed for explainability of the query answers. We tackle this challenge by adapting an existing proof framework toward conjunctive query answering, based on the notion of universal models. We investigate the data and combined…
Millennium Institute for Foundational Research on Data（千年基础数据研究研究所）；University of Chile（智利大学）；TU Wien（维也纳工业大学）；University of Bremen（不来梅大学）；University of Edinburgh（爱丁堡大学）
We focus on ontology-mediated queries (OMQs) based on (frontier-)guarded existential rules and (unions of) conjunctive queries, and we investigate the problem of FO-rewritability, i.e., whether an OMQ can be rewritten as a first-order query. We adopt two different approaches. The first approach employs standard two-way alternating parity tree automata. Although it does not lead to a tight complexity bound, it provides a transparent solution based on widely known tools. The second approach relies on a sophisticated automata model, known as cost automata. This allows us to show that our problem …
LIRMM, CNRS（法国国家科学研究中心LIRMM实验室）；Birkbeck, University of London（伦敦大学伯贝克学院）；Steklov Mathematical Institute, Moscow（莫斯科斯捷克洛夫数学研究所）
We give solutions to two fundamental computational problems in ontology-based data access with the W3C standard ontology language OWL 2 QL: the succinctness problem for first-order rewritings of ontology-mediated queries (OMQs), and the complexity problem for OMQ answering. We classify OMQs according to the shape of their conjunctive queries (treewidth, the number of leaves) and the existential depth of their ontologies. For each of these classes, we determine the combined complexity of OMQ answering, and whether all OMQs in the class have polynomial-size first-order, positive existential, and…
DCC, U of Chile & IMFD Chile（智利大学计算机系与智利千年数据基金会）；University of Bremen（不来梅大学）；University of Edinburgh（爱丁堡大学）
In ontology-mediated querying, description logic (DL) ontologies are used to enrich incomplete data with domain knowledge which results in more complete answers to queries. However, the evaluation of ontology-mediated queries (OMQs) over relational databases is computationally hard. This raises the question when OMQ evaluation is efficient, in the sense of being tractable in combined complexity or fixed-parameter tractable. We study this question for a range of ontology-mediated query languages based on several important and widely-used DLs, using unions of conjunctive queries as the actual qu…
Aiming at ontology-based data access to temporal data, we design two-dimensional temporal ontology and query languages by combining logics from the (extended) DL-Lite family with linear temporal logic LTL over discrete time (Z,<). Our main concern is first-order rewritability of ontology-mediated queries (OMQs) that consist of a 2D ontology and a positive temporal instance query. Our target languages for FO-rewritings are two-sorted FO(<) - first-order logic with sorts for time instants ordered by the built-in precedence relation < and for the domain of individuals - its extension FOE with the…
Tianjin University（天津大学）；Western Sydney University（西悉尼大学）；Huazhong University of Technology and Science（华中科技大学）；University of Alberta（阿尔伯塔大学）；Nankai University（南开大学）
An ontology language for ontology mediated query answering (OMQA-language) is universal for a family of OMQA-languages if it is the most expressive one among this family. In this paper, we focus on three families of tractable OMQA-languages, including first-order rewritable languages and languages whose data complexity of the query answering is in AC0 or PTIME. On the negative side, we prove that there is, in general, no universal language for each of these families of languages. On the positive side, we propose a novel property, the locality, to approximate the first-order rewritability, and …
Center for Semantic Web Research（语义网研究中心）；University of Chile（智利大学）；TU Wien（维也纳工业大学）；University of Edinburgh（爱丁堡大学）
Many efforts have been dedicated to identifying restrictions on ontologies expressed as tuple-generating dependencies (tgds), a.k.a. existential rules, that lead to the decidability for the problem of answering ontology-mediated queries (OMQs). This has given rise to three families of formalisms: guarded, non-recursive, and sticky sets of tgds. In this work, we study the containment problem for OMQs expressed in such formalisms, which is a key ingredient for solving static analysis tasks associated with them. Our main contribution is the development of specially tailored techniques for OMQ con…
University of Liverpool（利物浦大学）；University of Bremen（不来梅大学）
We study the complexity of ontology-mediated querying when ontologies are formulated in the guarded fragment of first-order logic (GF). Our general aim is to classify the data complexity on the level of ontologies where query evaluation w.r.t. an ontology O is considered to be in PTime if all (unions of conjunctive) queries can be evaluated in PTime w.r.t. O and coNP-hard if at least one query is coNP-hard w.r.t. O. We identify several large and relevant fragments of GF that enjoy a dichotomy between PTime and coNP, some of them additionally admitting a form of counting. In fact, almost all on…
In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology. To correctly compute answers to queries, it is necessary to perform complex reasoning over the constraints expressed by the ontology. In the literature, there exists a multitude of techniques incorporating the ontological knowledge into queries. However, few of these approaches were designed for comprehensibility of the query answers. In this article, we try to bridge these two qualities by adapting a proof framework originally applied to axiom entailment for co…
Big Data architectures allow to flexibly store and process heterogeneous data, from multiple sources, in their original format. The structure of those data, commonly supplied by means of REST APIs, is continuously evolving. Thus data analysts need to adapt their analytical processes after each API release. This gets more challenging when performing an integrated or historical analysis. To cope with such complexity, in this paper, we present the Big Data Integration ontology, the core construct to govern the data integration process under schema evolution by systematically annotating it with in…
Our concern is the overhead of answering OWL 2 QL ontology-mediated queries (OMQs) in ontology-based data access compared to evaluating their underlying tree-shaped and bounded treewidth conjunctive queries (CQs). We show that OMQs with bounded-depth ontologies have nonrecursive datalog (NDL) rewritings that can be constructed and evaluated in LOGCFL for combined complexity, even in NL if their CQs are tree-shaped with a bounded number of leaves, and so incur no overhead in complexity-theoretic terms. For OMQs with arbitrary ontologies and bounded-leaf CQs, NDL-rewritings are constructed and e…
IMC, PUC Chile（智利天主教大学IMC）；IMFD Chile（智利数学建模研究所）；Universitat Pompeu Fabra（庞培法布拉大学）；University of Bremen（不来梅大学）；University of Edinburgh（爱丁堡大学）
Ontology-mediated querying and querying in the presence of constraints are two key database problems where tuple-generating dependencies (TGDs) play a central role. In ontology-mediated querying, TGDs can formalize the ontology and thus derive additional facts from the given data, while in querying in the presence of constraints, they restrict the set of admissible databases. In this work, we study the limits of efficient query evaluation in the context of the above two problems, focussing on guarded and frontier-guarded TGDs and on UCQs as the actual queries. We show that a class of ontology-…
Free University of Bozen-Bolzano（博尔扎诺自由大学）；Umeå University（于默奥大学）；Max-Planck-Institut für Informatik（马克斯·普朗克计算机科学研究所）
Counting answers to a query is an operation supported by virtually all database management systems. In this paper we focus on counting answers over a Knowledge Base (KB), which may be viewed as a database enriched with background knowledge about the domain under consideration. In particular, we place our work in the context of Ontology-Mediated Query Answering/Ontology-based Data Access (OMQA/OBDA), where the language used for the ontology is a member of the DL-Lite family and the data is a (usually virtual) set of assertions. We study the data complexity of query answering, for different memb…
Existential rules are a very popular ontology-mediated query language for which the chase represents a generic computational approach for query answering. It is straightforward that existential rule queries exhibiting chase termination are decidable and can only recognize properties that are preserved under homomorphisms. In this paper, we show the converse: every decidable query that is closed under homomorphism can be expressed by an existential rule set for which the standard chase universally terminates. Membership in this fragment is not decidable, but we show via a diagonalisation argume…
Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge. For querying the absence of information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closed-world assumption, and therefore are not suited to deal with the anonymous objects that are common in ontological reasoning. Many real-world applications, like processing electronic health records (EHRs), also contain a temporal dimension, and require efficient reasoning algorithms. Moreover, since medical data is no…
University of Bordeaux（波尔多大学）；CNRS（法国国家科学研究中心）；Bordeaux INP（波尔多国立理工学院）；LaBRI（波尔多计算机科学研究实验室）；Inria（法国国家信息与自动化研究所）；DI ENS（巴黎高等师范学院计算机系）；ENS（巴黎高等师范学院）；University PSL（巴黎文理研究大学）
Ontology-mediated query answering (OMQA) is a promising approach to data access and integration that has been actively studied in the knowledge representation and database communities for more than a decade. The vast majority of work on OMQA focuses on conjunctive queries, whereas more expressive queries that feature counting or other forms of aggregation remain largely unex-plored. In this paper, we introduce a general form of counting query, relate it to previous proposals, and study the complexity of answering such queries in the presence of DL-Lite ontologies. As it follows from existing w…
A General Sufficient Condition for Rewriting Horn-ALCHI Atomic Queries into GQL
LIRMM（蒙彼利埃计算机科学、机器人学与微电子实验室）；Inria（法国国家信息与自动化研究所）；University of Montpellier（蒙彼利埃大学）；CNRS（法国国家科学研究中心）；DI ENS（巴黎高等师范学院信息学系）；ENS（巴黎高等师范学院）；PSL University（巴黎文理研究大学）
Ontology-Mediated Query Answering (OMQA) is a well-established framework to answer queries over an RDFS or OWL Knowledge Base (KB). OMQA was originally designed for unions of conjunctive queries (UCQs), and based on certain answers. More recently, OMQA has been extended to SPARQL queries, but to our knowledge, none of the efforts made in this direction (either in the literature, or the so-called SPARQL entailment regimes) is able to capture both certain answers for UCQs and the standard interpretation of SPARQL over a plain graph. We formalize these as requirements to be met by any semantics a…
We study the parameterized complexity of evaluating Ontology Mediated Queries (OMQs) based on Guarded TGDs (GTGDs) and Unions of Conjunctive Queries (UCQs), in the case where relational symbols have unrestricted arity and where the parameter is the size of the OMQ. We establish exact criteria for fixed-parameter tractability (fpt) evaluation of recursively enumerable classes of such OMQs (under the widely held Exponential Time Hypothesis). One of the main technical tools introduced in the paper is an fpt-reduction from deciding parameterized uniform CSPs to parameterized OMQ evaluation. The re…
