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.

Peer-Daten-Management-Systeme (PDMS) bestehen aus einer hochdynamischen Menge heterogener, autonomer Peers. Die Peers beantworten Anfragen einerseits gegen lokal gespeicherte Daten und reichen sie andererseits nach einer Umschreibung anhand von Schema-Mappings an benachbarte Peers weiter. Solche aufgrund fehlender zentraler Komponenten eigentlich hoch- flexiblen Systeme leiden bei zunehmender Anzahl von Peers unter erheblichen Effi- zienzproblemen. Die Gründe hierfür liegen in der massiven Redundanz der Pfade im Netzwerk der Peers und im Informationsverlust aufgrund von Projektionen entlang von Mapping-Pfaden. Anwender akzeptieren in hochskalierten Umgebungen zum Datenaustausch in vielen Anwendungsszenarien Konzessionen an die Vollständigkeit der Anfrageergebnisse. Unser Ansatz sieht in der Vollständigkeit ein Optimierungsziel und verfolgt einen Kompromiß zwischen Nutzen und Kosten der Anfragebearbeitung. Hierzu schlagen wir mehrere Strategien für Peers vor, um zu entscheiden, an welche Nachbar-Peers Anfragen weitergeleitet werden. Peers schließen dabei Mappings von der Anfragebearbeitung aus, von denen sie ein geringes Verhältnis von Ergebnisgröße zu Kosten, also geringe Effizienz erwarten. Als Basis dieser Schätzungen wenden wir selbstadaptive Histogramme über die Ergebniskardinalität an und weisen nach, daß diese in dieser hochdynamischen Umgebung ausreichende Genauigkeit aufweisen. Wir schlagen einen Kompromiß zwischen der Nutzung von Anfrageergebnissen zur Anpassung dieser Metadaten-Statistiken und der Beschneidung von Anfrageplänen vor, um den entsprechenden Zielkonflikt aufzulösen. Für eine Optimierungsstrategie, die das für die Anfragebearbeitung verwendete Zeit-Budget limitiert, untersuchen wir mehrere Varianten hinsichtlich des Effizienzsteigerungspotentials. Darüber hinaus nutzen wir mehrdimensionale Histogramme über die Überlappung zweier Datenquellen zur gezielten Verminderung der Redundanz in der Anfragebearbeitung. / Peer data management systems (PDMS) consist of a highly dynamic set of autonomous, heterogeneous peers connected with schema mappings. Queries submitted at a peer are answered with data residing at that peer and by passing the queries to neighboring peers. PDMS are the most general architecture for distributed integrated information systems. With no need for central coordination, PDMS are highly flexible. However, due to the typical massive redundancy in mapping paths, PDMS tend to be very inefficient in computing the complete query result as the number of peers increases. Additionally, information loss is cumulated along mapping paths due to selections and projections in the mappings. Users usually accept concessions on the completeness of query answers in large-scale data sharing settings. Our approach turns completeness into an optimization goal and thus trades off benefit and cost of query answering. To this end, we propose several strategies that guide peers in their decision to which neighbors rewritten queries should be sent. In effect, the peers prune mappings that are expected to contribute few data. We propose a query optimization strategy that limits resource consumption and show that it can drastically increase efficiency while still yielding satisfying completeness of the query result. To estimate the potential data contribution of mappings, we adopted self-tuning histograms for cardinality estimation. We developed techniques that ensure sufficient query feedback to adapt these statistics to massive changes in a PDMS. Additionally, histograms can serve to maintain statistics on data overlap between alternative mapping paths. Building on them, redundant query processing is reduced by avoiding overlapping areas of the multi-dimensional data space.

We study the approximate answers to OLAP queries on data warehouses. We consider the relative answers to OLAP queries on a schema, as distributions with the L1 distance and approximate the answers without storing the entire data warehouse. We first introduce three specific methods: the uniform sampling, the measure-based sampling and the statistical model. We introduce also an edit distance between data warehouses with edit operations adapted for data warehouses. Then, in the OLAP data exchange, we study how to sample each source and combine the samples to approximate any OLAP query. We next consider a streaming context, where a data warehouse is built by streams of different sources. We show a lower bound on the size of the memory necessary to approximate queries. In this case, we approximate OLAP queries with a finite memory. We describe also a method to discover the statistical dependencies, a new notion we introduce. We are looking for them based on the decision tree. We apply the method to two data warehouses. The first one simulates the data of sensors, which provide weather parameters over time and location from different sources. The second one is the collection of RSS from the web sites on Internet.

Les contraintes sont les artéfacts fondamentaux permettant de donner un sens aux données. Elles garantissent que les données sont conformes aux besoins des applications. L'objet de cette thèse est d'étudier deux problématiques liées à la gestion efficace des données en présence de contraintes. Nous abordons le problème de répondre efficacement à des requêtes portant sur des données, en présence de contraintes déductives. Cela mène à des données implicites dérivant de données explicites et de contraintes. Les données implicites requièrent une étape de raisonnement afin de calculer les réponses aux requêtes. Le raisonnement par reformulation des requêtes compile les contraintes dans une requête modifiée qui, évaluée à partir des données explicites uniquement, génère toutes les réponses fondées sur les données explicites et implicites. Comme les requêtes reformulées peuvent être complexes, leur évaluation est souvent difficile et coûteuse. Nous étudions l'optimisation de la technique de réponse aux requêtes par reformulation dans le cadre de l'accès aux données à travers une ontologie, où des requêtes conjonctives SPARQL sont posées sur un ensemble de faits RDF sur lesquels des contraintes RDF Schema (RDFS) sont exprimées. La thèse apporte les contributions suivantes. (i) Nous généralisons les langages de reformulation de requêtes précédemment étudiées, afin d'obtenir un espace de reformulations d'une requête posée plutôt qu'une unique reformulation. (ii) Nous présentons des algorithmes effectifs et efficaces, fondés sur un modèle de coût, permettant de sélectionner une requête reformulée ayant le plus faible coût d'évaluation. (iii) Nous montrons expérimentalement que notre technique améliore significativement la performance de la technique de réponse aux requêtes par reformulation. Au-delà de RDFS, nous nous intéressons aux langages d'ontologie pour lesquels répondre à une requête peut se réduire à l'évaluation d'une certaine formule de la Logique du Premier Ordre (obtenue à partir de la requête et de l'ontologie), sur les faits explicites uniquement. (iv) Nous généralisons la technique de reformulation optimisée pour RDF, mentionnée ci-dessus, aux formalismes pour répondre à une requête LPO-réductible. (v) Nous appliquons cette technique à la Logique de Description DL-LiteR sous-jacente au langage OWL2 QL du W3C, et montrons expérimentalement ses avantages dans ce contexte. Nous présentons également, brièvement, un travail en cours sur le problème consistant à fournir des chemins d'accès efficaces aux données dans les systèmes Big Data. Nous proposons d'utiliser un ensemble de systèmes de stockages hétérogènes afin de fournir une meilleure performance que n'importe lequel d'entre eux, utilisé individuellement. Les données stockées dans chaque système peuvent être décrites comme des vues matérialisées sur les données applicatives. Répondre à une requête revient alors à réécrire la requête à l'aide des vues disponibles, puis à décoder la réécriture produite comme un ensemble de requêtes à exécuter sur les systèmes stockant les vues, ainsi qu'une requête les combinant de façon appropriée. / Constraints are the essential artefact for giving meaning to data, ensuring that it fits real-life application needs, and that its meaning is correctly conveyed to the users. This thesis investigates two fundamental problems related to the efficient management of data in the presence of constraints. We address the problem of efficiently answering queries over data in the presence of deductive constraints, which lead to implicit data that is entailed (derived) from the explicit data and the constraints. Implicit data requires a reasoning step in order to compute complete query answers, and two main query answering techniques exist. Data saturation compiles the constraints into the database by making all implicit data explicit, while query reformulation compiles the constraints into a modified query, which, evaluated over the explicit data only, computes all the answer due to explicit and/or implicit data. So far, reformulation-based query answering has received significantly less attention than saturation. In particular, reformulated queries may be complex, thus their evaluation may be very challenging. We study optimizing reformulation-based query answering in the setting of ontology-based data access, where SPARQL conjunctive queries are answered against a set of RDF facts on which constraints hold. When RDF Schema is used to express the constraints, the thesis makes the following contributions. (i) We generalize prior query reformulation languages, leading to a space of reformulated queries we call JUCQs (joins of unions of conjunctive queries), instead of a single fixed reformulation. (ii) We present effective and efficient cost-based algorithms for selecting from this space, a reformulated query with the lowest estimated cost. (iii) We demonstrate through experiments that our technique drastically improves the performance of reformulation-based query answering while always avoiding “worst-case” performance. Moving beyond RDFS, we consider the large and useful set of ontology languages enjoying FOL reducibility of query answering: answering a query can be reduced to evaluating a certain first-order logic (FOL) formula (obtained from the query and ontology) against only the explicit facts. (iv) We generalize the above-mentioned JUCQ-based optimized reformulation technique to improve performance in any FOL-reducible setting, and (v) we instantiate this framework to the DL-LiteR Description Logic underpinning the W3C’s OWL2 QL ontology language, demonstrating significant performance advantages in this setting also. We also report on current work regarding the problem of providing efficient data access paths in Big Data stores. We consider a setting where a set of different, heterogeneous storage systems can be used side by side to provide better performance than any of them used individually. In such a setting, the data stored in each system can be described as views over the application data. Answering a query thus amounts to rewrite the query using the available views, and then to decode the rewriting into a set of queries to be executed on the systems holding the views, and a query combining them appropriately.

Probabilistic data and knowledge bases are becoming increasingly important in academia and industry. They are continuously extended with new data, powered by modern information extraction tools that associate probabilities with knowledge base facts. The state of the art to store and process such data is founded on probabilistic database systems, which are widely and successfully employed. Beyond all the success stories, however, such systems still lack the fundamental machinery to convey some of the valuable knowledge hidden in them to the end user, which limits their potential applications in practice. In particular, in their classical form, such systems are typically based on strong, unrealistic limitations, such as the closed-world assumption, the closed-domain assumption, the tuple-independence assumption, and the lack of commonsense knowledge. These limitations do not only lead to unwanted consequences, but also put such systems on weak footing in important tasks, querying answering being a very central one. In this thesis, we enhance probabilistic data and knowledge bases with more realistic data models, thereby allowing for better means for querying them. Building on the long endeavor of unifying logic and probability, we develop different rigorous semantics for probabilistic data and knowledge bases, analyze their computational properties and identify sources of (in)tractability and design practical scalable query answering algorithms whenever possible. To achieve this, the current work brings together some recent paradigms from logics, probabilistic inference, and database theory.

In this thesis, we study the notion of graph summarization, which is a fundamental task of finding a compact representation of the original graph called the summary. Graph summarization can be used for reducing the footprint of the input graph, better visualization, anonymizing the identity of users, and query answering. There are two different frameworks of graph summarization we consider in this thesis, the utility-based framework and the correction set-based framework. In the utility-based framework, the input graph is summarized until a utility threshold is not violated. In the correction set-based framework a set of correction edges is produced along with the summary graph. In this thesis we propose two algorithms for the utility-based framework and one for the correction set-based framework. All these three algorithms are for static graphs (i.e. graphs that do not change over time). Then, we propose two more utility-based algorithms for fully dynamic graphs (i.e. graphs with edge insertions and deletions). Algorithms for graph summarization can be lossless (summarizing the input graph without losing any information) or lossy (losing some information about the input graph in order to summarize it more). Some of our algorithms are lossless and some lossy, but with controlled utility loss. Our first utility-driven graph summarization algorithm, G-SCIS, is based on a clique and independent set decomposition, that produces optimal compression with zero loss of utility. The compression provided is significantly better than state-of-the-art in lossless graph summarization, while the runtime is two orders of magnitude lower. Our second algorithm is T-BUDS, a highly scalable, utility-driven algorithm for fully controlled lossy summarization. It achieves high scalability by combining memory reduction using Maximum Spanning Tree with a novel binary search procedure. T-BUDS outperforms state-of-the-art drastically in terms of the quality of summarization and is about two orders of magnitude better in terms of speed. In contrast to the competition, we are able to handle web-scale graphs in a single machine without performance impediment as the utility threshold (and size of summary) decreases. Also, we show that our graph summaries can be used as-is to answer several important classes of queries, such as triangle enumeration, Pagerank and shortest paths. We then propose algorithm LDME, a correction set-based graph summarization algorithm that produces compact output representations in a fast and scalable manner. To achieve this, we introduce (1) weighted locality sensitive hashing to drastically reduce the number of comparisons required to find good node merges, (2) an efficient way to compute the best quality merges that produces more compact outputs, and (3) a new sort-based encoding algorithm that is faster and more robust. More interestingly, our algorithm provides performance tuning settings to allow the option of trading compression for running time. On high compression settings, LDME achieves compression equal to or better than the state of the art with up to 53x speedup in running time. On high speed settings, LDME achieves up to two orders of magnitude speedup with only slightly lower compression. We also present two lossless summarization algorithms, Optimal and Scalable, for summarizing fully dynamic graphs. More concretely, we follow the framework of G-SCIS, which produces summaries that can be used as-is in several graph analytics tasks. Different from G-SCIS, which is a batch algorithm, Optimal and Scalable are fully dynamic and can respond rapidly to each change in the graph. Not only are Optimal and Scalable able to outperform G-SCIS and other batch algorithms by several orders of magnitude, but they also significantly outperform MoSSo, the state-of-the-art in lossless dynamic graph summarization. While Optimal produces always the most optimal summary, Scalable is able to trade the amount of node reduction for extra scalability. For reasonable values of the parameter $K$, Scalable is able to outperform Optimal by an order of magnitude in speed, while keeping the rate of node reduction close to that of Optimal. An interesting fact that we observed experimentally is that even if we were to run a batch algorithm, such as G-SCIS, once for every big batch of changes, still they would be much slower than Scalable. For instance, if 1 million changes occur in a graph, Scalable is two orders of magnitude faster than running G-SCIS just once at the end of the 1 million-edge sequence. / Graduate

We present some initial results on ontology-based query answering with description logic ontologies that may employ temporal and probabilistic operators on concepts and axioms. Speci_cally, we consider description logics extended with operators from linear temporal logic (LTL), as well as subjective probability operators, and an extended query language in which conjunctive queries can be combined using these operators. We first show some complexity results for the setting in which either only temporal operators or only probabilistic operators may be used, both in the ontology and in the query, and then show a 2ExpSpace lower bound for the setting in which both types of operators can be used together. / This is an extended version of an article accepted at Description Logics 2019.

We present a method for answering ontology-mediated queries for DL-Lite extended with a concrete domain, where we allow concrete domain predicates to be used in the query as well. Our method is based on query rewriting, a well-known technique for ontology-based query answering (OBQA), where the knowledge provided by the ontology is compiled into the query so that the rewritten query can be evaluated directly over a database. This technique reduces the problem of query answering w.r.t. an ontology to query evaluation over a database instance. Specifically, we consider members of the DL-Lite family extended with unary and binary concrete domain predicates over the real numbers. While approaches for query rewriting DL-Lite with these concrete domain have been investigated theoretically, these approaches use a combined approach in which also the data is processed, and require the concrete domain values occurring in the data to be known in advance, which makes the procedure data-dependent. In contrast, we show how rewritings can be computed in a data-independent fashion.

We investigate ontology-based query answering (OBQA) in a setting where both the ontology and the query can refer to concrete values such as numbers and strings. In contrast to previous work on this topic, the built-in predicates used to compare values are not restricted to being unary. We introduce restrictions on these predicates and on the ontology language that allow us to reduce OBQA to query answering in databases using the so-called combined rewriting approach. Though at first sight our restrictions are different from the ones used in previous work, we show that our results strictly subsume some of the existing first-order rewritability results for unary predicates. / This is an extended version of a paper published in the proceedings of IJCAI 2017.

We consider ontology-based query answering in a setting where some of the data are numerical and of a probabilistic nature, such as data obtained from uncertain sensor readings. The uncertainty for such numerical values can be more precisely represented by continuous probability distributions than by discrete probabilities for numerical facts concerning exact values. For this reason, we extend existing approaches using discrete probability distributions over facts by continuous probability distributions over numerical values. We determine the exact (data and combined) complexity of query answering in extensions of the well-known description logics EL and ALC with numerical comparison operators in this probabilistic setting. / This is an extended version of the article in: Proceedings of the 11th International Symposium on Frontiers of Combining Systems. This version has been revised based on the comments of the reviewers.