Ontology-mediated Query Research Articles

Data Access With Horn Ontologies: Where Description Logics Meet Existential Rules

Two main families of ontology languages are considered in the context of data access, namely Horn description logics and existential rules. In this paper, we review the semantic relationships between these families in the light of the ontology-mediated query answering problem. To this end, we rely on the standard translation of description logics in first-order logic and on the notion of semantic emulation. We focus on description logics and classes of existential rules for which the con-junctive query answering problem has polynomial data complexity.

Ontology-Mediated Querying with Horn Description Logics

An ontology-mediated query (OMQ) consists of a database query paired with an ontology. When evaluated on a database, an OMQ returns not only the answers that are already in the database, but also those answers that can be obtained via logical reasoning using rules from ontology. There are many open questions regarding the complexities of problems related to OMQs. Motivated by the use of ontologies in practice, new reasoning problems which have never been considered in the context of ontologies become relevant, since they can improve the usability of ontology enriched systems. This thesis deals with various reasoning problems that emerge from ontology-mediated querying and it investigates the computational complexity of these problems. We focus on ontologies formulated in Horn description logics, which are a popular choice for ontologies in practice. In particular, the thesis gives results regarding the data complexity of OMQ evaluation by completely classifying complexity and rewritability questions for OMQs based on an EL ontology and a conjunctive query. Furthermore, the query-by-example problem, and the expressibility and verification problem in ontology-based data access are introduced and investigated.

Rewriting Approaches for Ontology-Mediated Query Answering

A most promising approach to answering queries in ontology-based data access (OBDA) is through query rewriting. In this paper we present novel rewriting approaches for several extensions of OBDA. The goal is to understand their relative expressiveness and to pave the way for efficient query answering algorithms.

Characterizing Boundedness in Chase Variants

AbstractExistential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions.

Query Rewriting for Ontology-Mediated Conditional Answers

Among many solutions for extracting useful answers from incomplete data, ontology-mediated queries (OMQs) use domain knowledge to infer missing facts. We propose an extension of OMQs that allows us to make certain assumptions—for example, about parts of the data that may be unavailable at query time, or costly to query—and retrieve conditional answers, that is, tuples that become certain query answers when the assumptions hold. We show that querying in this powerful formalism often has no higher worst-case complexity than in plain OMQs, and that these queries are first-order rewritable for DL-Liteℛ. Rewritability is preserved even if we allow some use of closed predicates to combine the (partial) closed- and open-world assumptions. This is remarkable, as closed predicates are a very useful extension of OMQs, but they usually make query answering intractable in data complexity, even in very restricted settings.

Towards Universal Languages for Tractable Ontology Mediated Query Answering

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 show that there exists a language of disjunctive embedded dependencies that is universal for the family of OMQA-languages with locality. All of these results apply to OMQA with query languages such as conjunctive queries, unions of conjunctive queries and acyclic conjunctive queries.

Polynomial rewritings from expressive Description Logics with closed predicates to variants of Datalog

In many scenarios, complete and incomplete information coexist. For this reason, the knowledge representation and database communities have long shown interest in simultaneously supporting the closed- and the open-world views when reasoning about logic theories. Here we consider the setting of querying possibly incomplete data using logic theories, formalized as the evaluation of an ontology-mediated query (OMQ) that pairs a query with a theory, sometimes called an ontology, expressing background knowledge. This can be further enriched by specifying a set of closed predicates from the theory that are to be interpreted under the closed-world assumption, while the rest are interpreted with the open-world view. In this way we can retrieve more precise answers to queries by leveraging the partial completeness of the data.The central goal of this paper is to understand the relative expressiveness of ontology-mediated query languages in which the ontology part is written in the expressive Description Logic (DL) ALCHOI and includes a set of closed predicates. We consider a restricted class of conjunctive queries. Our main result is to show that every query in this non-monotonic query language can be translated in polynomial time into Datalog with negation as failure under the stable model semantics. To overcome the challenge that Datalog has no direct means to express the existential quantification present in ALCHOI, we define a two-player game that characterizes the satisfaction of the ontology, and design a Datalog query that can decide the existence of a winning strategy for the game. If there are no closed predicates—in the case of querying an ALCHOI knowledge base—our translation yields a positive disjunctive Datalog program of polynomial size. To the best of our knowledge, unlike previous translations for related fragments with expressive (non-Horn) DLs, these are the first polynomial time translations.

Ontology-Mediated Query Answering over Log-Linear Probabilistic Data

Large-scale knowledge bases are at the heart of modern information systems. Their knowledge is inherently uncertain, and hence they are often materialized as probabilistic databases. However, probabilistic database management systems typically lack the capability to incorporate implicit background knowledge and, consequently, fail to capture some intuitive query answers. Ontology-mediated query answering is a popular paradigm for encoding commonsense knowledge, which can provide more complete answers to user queries. We propose a new data model that integrates the paradigm of ontology-mediated query answering with probabilistic databases, employing a log-linear probability model. We compare our approach to existing proposals, and provide supporting computational results.

Ontology-mediated query answering over temporal and inconsistent data

Stream-based reasoning systems process data stemming from different sources that are received over time. In this kind of applications, reasoning needs to cope with the temporal dimension and should be resilient against inconsistencies in the data. Motivated by such settings, this paper addresses the problem of handling inconsistent data in a temporal version of ontology-mediated query answering. We consider a recently proposed temporal query language that combines conjunctive queries with operators of propositional linear temporal logic (LTL), and consider these under three inconsistency-tolerant semantics that have been introduced for querying inconsistent description logic knowledge bases. We investigate their complexity for temporal EL ⊥ and DL-LiteR knowledge bases. In particular, we consider two different cases, depending on the presence of negations in the query. Furthermore, we complete the complexity picture for the consistent case. We also provide two approaches toward practical algorithms for inconsistency-tolerant temporal query answering.

Querying Log Data with Metric Temporal Logic


 
 
 We propose a novel framework for ontology-based access to temporal log data using a datalog extension datalogMTL of the Horn fragment of the metric temporal logic MTL. We show that datalogMTL is EXPSPACE-complete even with punctual intervals, in which case full MTL is known to be undecidable. We also prove that nonrecursive datalogMTL is PSPACE-complete for combined complexity and in AC0 for data complexity. We demonstrate by two real-world use cases that nonrecursive datalogMTL programs can express complex temporal concepts from typical user queries and thereby facilitate access to temporal log data. Our experiments with Siemens turbine data and MesoWest weather data show that datalogMTL ontology-mediated queries are efficient and scale on large datasets.
 
 

Ontology-Mediated Queries

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 nonrecursive datalog rewritings. We obtain the succinctness results using hypergraph programs, a new computational model for Boolean functions, which makes it possible to connect the size of OMQ rewritings and circuit complexity.

An integration-oriented ontology to govern evolution in Big Data ecosystems

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 information regarding the schema of the sources. We present a query rewriting algorithm that, using the annotated ontology, converts queries posed over the ontology to queries over the sources. To cope with syntactic evolution in the sources, we present an algorithm that semi-automatically adapts the ontology upon new releases. This guarantees ontology-mediated queries to correctly retrieve data from the most recent schema version as well as correctness in historical queries. A functional and performance evaluation on real-world APIs is performed to validate our approach.

Query Answering in DL-Lite with Datatypes: A Non-Uniform Approach

Adding datatypes to ontology-mediated queries (OMQs) often makes query answering hard. As a consequence, the use of datatypes in OWL 2 QL has been severely restricted. In this paper we propose a new, non-uniform, way of analyzing the data-complexity of OMQ answering with datatypes. Instead of restricting the ontology language we aim at a classification of the patterns of datatype atoms in OMQs into those that can occur in non-tractable OMQs and those that only occur in tractable OMQs. To this end we establish a close link between OMQ answering with datatypes and constraint satisfaction problems over the datatypes. In a case study we apply this link to prove a P/coNP-dichotomy for OMQs over DL-Lite extended with the datatype (Q,<=). The proof employs a recent dichotomy result by Bodirsky and Kára for temporal constraint satisfaction problems.

Ontology-Mediated Queries for Probabilistic Databases

Probabilistic databases (PDBs) are usually incomplete, e.g., containing only the facts that have been extracted from the Web with high confidence. However, missing facts are often treated as being false, which leads to unintuitive results when querying PDBs. Recently, open-world probabilistic databases (OpenPDBs) were proposed to address this issue by allowing probabilities of unknown facts to take any value from a fixed probability interval. In this paper, we extend OpenPDBs by Datalog+/- ontologies, under which both upper and lower probabilities of queries become even more informative, enabling us to distinguish queries that were indistinguishable before. We show that the dichotomy between P and PP in (Open)PDBs can be lifted to the case of first-order rewritable positive programs (without negative constraints); and that the problem can become NP^PP-complete, once negative constraints are allowed. We also propose an approximating semantics that circumvents the increase in complexity caused by negative constraints.

Ontology-Based Data Access with a Horn Fragment of Metric Temporal Logic

We advocate datalogMTL, a datalog extension of a Horn fragment of the metric temporal logic MTL, as a language for ontology-based access to temporal log data. We show that datalogMTL is EXPSPACE-complete even with punctual intervals, in which case MTL is known to be undecidable. Nonrecursive datalogMTL turns out to be PSPACE-complete for combined complexity and in AC0 for data complexity. We demonstrate by two real-world use cases that nonrecursive datalogMTL programs can express complex temporal concepts from typical user queries and thereby facilitate access to log data. Our experiments with Siemens turbine data and MesoWest weather data show that datalogMTL ontology-mediated queries are efficient and scale on large datasets of up to 11GB.

Ontology-Mediated Queries for NOSQL Databases

Ontology-Based Data Access has been studied so far for relational structures and deployed on top of relational databases. This paradigm enables a uniform access to heterogeneous data sources, also coping with incomplete information. Whether OBDA is suitable also for non-relational structures, like those shared by increasingly popular NOSQL languages, is still an open question. In this paper, we study the problem of answering ontology-mediated queries on top of key-value stores. We formalize the data model and core queries of these systems, and introduce a rule language to express lightweight ontologies on top of data. We study the decidability and data complexity of query answering in this setting.

Ontology-Based Data Access

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 article, 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 of the article are threefold. First, we show that popular ontology-mediated query languages have the same expressive power as natural fragments of disjunctive datalog, and we study the relative succinctness of ontology-mediated queries and disjunctive datalog queries. Second, we establish intimate connections between ontology-mediated queries and constraint satisfaction problems (CSPs) and their logical generalization, MMSNP formulas. Third, we exploit these connections to obtain new results regarding: (i) first-order rewritability and datalog rewritability of ontology-mediated queries; (ii) P/NP dichotomies for ontology-mediated queries; and (iii) the query containment problem for ontology-mediated queries.