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Querying existential rule knowledge bases : decidability and complexity / Interrogation de bases de connaissances avec règles existentielles : décidabilité et complexitéRocher, Swan 25 November 2016 (has links)
Dans cette thèse, nous nous intéressons au problème d'interrogation de bases de connaissances composées de données et d'une ontologie, qui représente des connaissances générales sur le domaine d'application. Parmi les différents formalismes permettant de représenter les connaissances ontologiques, nous considérons ici un fragment de la logique du premier ordre appelé règles existentielles (aussi connues sous le nom de ``tuple generating dependencies'' et Datalog+/-). Le problème fondamental de conséquence logique au cœur de cette thèse demande si une requête conjonctive est conséquence d'une base de connaissances. Les règles existentielles étant très expressives, ce problème est indécidable. Toutefois, différentes restrictions sur les ensembles de règles ont été proposées afin d'obtenir sa décidabilité.La contribution de cette thèse est double. Premièrement, nous proposons un outil qui nous permet d'unifier puis d'étendre la plupart des classes de règles connues reposant sur des notions d'acyclicité assurant la finitude du chaînage avant. Deuxièmement, nous étudions la compatibilité des classes décidables de règles existentielles connues avec un type de connaissance souvent nécessaire dans les ontologies: la transitivité de relations binaires. Nous aidons à clarifier le paysage des résultats positifs et négatifs liés à cette question et fournissons une approche permettant de combiner la transitivité avec les règles existentielles linéaires. / In this thesis we investigate the issue of querying knowledge bases composed of data and general background knowledge, called an ontology. Ontological knowledge can be represented under different formalisms and we consider here a fragment of first-order logic called existential rules (also known as tuple-generating dependencies and Datalog+/-).The fundamental entailment problem at the core of this thesis asks if a conjunctive query is entailed by an existential rule knowledge base. General existential rules are highly expressive, however at the cost of undecidability. Various restrictions on sets of rules have been proposed to regain the decidability of the entailment problem.Our specific contribution is two-fold. First, we propose a new tool that allows to unify and extend most of the known existential rule classes that rely on acyclicity conditions to tame infinite forward chaining, without increasing the complexity of the acyclicity recognition. Second, we study the compatibility of known decidable rule classes with a frequently required modeling construct, namely transitivity of binary relations. We help clarifying the picture of negative and positive results on this question, and provide a technique to safely combine transitivity with one of the simplest, yet useful, decidable rule classes, namely linear rules.
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Conjunctive query answering under existential rules : decidability, complexity and algorithms / Interrogation de bases de connaissances avec des règles expressives : décidabilité, complexité et algorithmesThomazo, Michaël 24 October 2013 (has links)
L'objectif du problème appelé "Ontology-based data access" (OBDA) est d'améliorer la réponse à des requêtes en prenant en compte des connaissances d'ordre général durant l'évaluation des requêtes. Ces connaissances générales sont représentées à l'aide d'une ontologie, qui est exprimée dans cette thèse grâce à des formules logiques du premier ordre, appelées règles existentielles, et aussi connues sous le nom de "tuple-generating dependencies" et Datalog+/-. L'expressivité des formules utilisées est telle que l'évaluation de requêtes devient un problème indécidable, et cela a conduit la communauté à définir de nombreux cas décidables, c'est-à-dire des restrictions sur les ensembles de règles existentielles considérés. La contribution de cette thèse est double : tout d'abord, nous proposons une vue unifiée sur une grande fraction des cas décidables connus, et fournissons par là même une analyse de complexité et un algorithme optimal dans le pire des cas. Nous considérons également l'approche couramment utilisée de réécriture de requêtes, et proposons un algorithme générique qui permet de surmonter certaines causes évidentes d'explosion combinatoire qui rendent les approches classiques pratiquement inapplicables. / Ontology-based data access (OBDA) aims at enriching query answering by taking general background knowledge into account when evaluating queries. This background knowledge is represented by means of an ontology, that is expressed in this thesis by a very expressive class of first-order formulas, called existential rules (sometimes also tuple-generating dependencies and Datalog+/-). The high expressivity of the used formalism results in the undecidability of query answering, and numerous decidable classes (that is, restrictions on the sets of existential rules) have been proposed in the literature. The contribution of this thesis is two-fold: first, we propose a unified view of a large part of these classes, together with a complexity analysis and a worst-case optimal algorithm for the introduced generic class. Second, we consider the popular approach of query rewriting, and propose a generic algorithm that overcomes trivial causes of combinatorial explosion that make classical approaches inapplicable.
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On Implementing Temporal Query Answering in DL-LiteThost, Veronika, Holste, Jan, Özçep, Özgür 20 June 2022 (has links)
Ontology-based data access augments classical query answering over fact bases by adopting the open-world assumption and by including domain knowledge provided by an ontology. We implemented temporal query answering w.r.t. ontologies formulated in the Description Logic DL-Lite. Focusing on temporal conjunctive queries (TCQs), which combine conjunctive queries via the operators of propositional linear temporal logic, we regard three approaches for answering them: an iterative algorithm that considers all data available; a window-based algorithm; and a rewriting approach, which translates the TCQs to be answered into SQL queries. Since the relevant ontological knowledge is already encoded into the latter queries, they can be answered by a standard database system. Our evaluation especially shows that implementations of both the iterative and the window-based algorithm answer TCQs within a few milliseconds, and that the former achieves a constant performance, even if data is growing over time.
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Temporal Query Answering in DL-Lite with NegationBorgwardt, Stefan, Thost, Veronika 20 June 2022 (has links)
Ontology-based query answering augments classical query answering in databases by adopting the open-world assumption and by including domain knowledge provided by an ontology. We investigate temporal query answering w.r.t. ontologies formulated in DL-Lite, a family of description logics that captures the conceptual features of relational databases and was tailored for efficient query answering. We consider a recently proposed temporal query language that combines conjunctive queries with the operators of propositional linear temporal logic (LTL). In particular, we consider negation in the ontology and query language, and study both data and combined complexity of query entailment.
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Answering Conjunctive Queries and FO+MOD Queries under UpdatesKeppeler, Jens 26 June 2020 (has links)
In dieser Arbeit wird das dynamische Auswertungsproblem über dynamische Datenbanken betrachtet, bei denen Tupel hinzugefügt oder gelöscht werden können. Die Aufgabe besteht darin einen dynamischen Algorithmus zu konstruieren, welcher unmittelbar nachdem die Datenbank aktualisiert wurde, die Datenstruktur, die das Resultat repräsentiert, aktualisiert.
Die Datenstruktur soll in konstanter Zeit aktualisiert werden und das Folgende unterstützen:
* Teste in konstanter Zeit ob ein Tupel zur Ausgabemenge gehört,
* gebe die Anzahl der Tupel in der Ausgabemenge in konstanter Zeit aus,
* zähle die Tupel aus der Ausgabemenge mit konstanter Taktung auf und
* zähle den Unterschied zwischen der neuen und der alten Ausgabemenge mit konstanter Taktung auf.
Im ersten Teil werden konjunktive Anfragen und Vereinigungen konjunktiver Anfragen auf relationalen Datenbanken betrachtet. Die Idee der q-hierarchischen Anfragen (und t-hierarchische Anfragen für das Testen) wird eingeführt und es wird gezeigt, dass das Resultat für jede q-hierarchische Anfrage auf dynamischen Datenbanken effizient in dem oben beschriebenen Szenario ausgewertet werden können. Konjunktive Anfragen mit Aggregaten werden weiterhin betrachtet. Es wird gezeigt, dass das Lernen von polynomiellen Regressionsfunktionen in konstanter Zeit vorbereitet werden kann, falls die Trainingsdaten aus dem Anfrageergebnis kommen.
Mit logarithmischer Update-Zeit kann folgende Routine unterstützt werden: Bei Eingabe einer Zahl j, gebe das j-te Tupel aus der Aufzählung aus.
Im zweiten Teil werden Anfragen, die Formeln der Logik erster Stufe (FO) und deren Erweiterung mit Modulo-Zähl Quantoren (FO+MOD) sind, betrachtet, und es wird gezeigt, dass diese effizient unter Aktualisierungen ausgewertet können, wobei die dynamische Datenbank die Gradschranke nicht überschreitet, und bei der Auswertung die Zähl-, Test-, Aufzähl- und die Unterschied-Routine unterstützt werden. / This thesis investigates the query evaluation problem for fixed queries over fully dynamic
databases, where tuples can be inserted or deleted.
The task is to design a dynamic algorithm that
immediately reports the new result of a fixed query after every database update.
In particular, the goal is to construct a data structure that allows to
support the following scenario.
After every database update, the data structure can be updated in
constant time such that afterwards we are able
* to test within constant time for a given tuple whether or not it belongs to the query result,
* to output the number of tuples in the query result,
* to enumerate all tuples in the new query result with constant delay and
* to enumerate the difference between the old and the new query result with constant delay.
In the first part, conjunctive queries and unions of conjunctive queries on arbitrary relational
databases are considered. The notion of q-hierarchical conjunctive queries (and t-hierarchical conjunctive queries for testing) is introduced and it is shown that the result of each such query on a dynamic database can be maintained efficiently in the sense described above. Moreover, this notion is extended to aggregate queries.
It is shown that the preparation of learning a polynomial regression function can be done
in constant time if the training data are taken (and maintained under updates) from the query result of
a q-hierarchical query.
With logarithmic update time the following
routine is supported: upon input of a natural number j, output the j-th tuple that will be enumerated.
In the second part, queries in first-order logic (FO) and its extension with modulo-counting quantifiers (FO+MOD) are considered, and it is shown that they can be efficiently evaluated under updates, provided that the dynamic database does not exceed a certain degree bound, and the counting, testing, enumeration and difference routines is supported.
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Temporal Conjunctive Queries in Expressive DLs with Non-simple RolesBaader, Franz, Borgwardt, Stefan, Lippmann, Marcel 20 June 2022 (has links)
In Ontology-Based Data Access (OBDA), user queries are evaluated over a set of facts under the open world assumption, while taking into account background knowledge given in the form of a Description Logic (DL) ontology. Motivated by situation awareness applications, temporal conjunctive queries (TCQs) have recently been proposed as a useful extension of traditional OBDA to support the processing of temporal information. This paper extends the existing complexity analysis of TCQ entailment to very expressive DLs underlying the OWL 2 standard, and in contrast to previous work also allows for queries containing transitive roles. / This is an extended version of the paper “Temporal Conjunctive Queries in Expressive Description Logics with Transitive Roles”, published in the Proceedings of the 28th Australasian Joint Conference on Artificial Intelligence (AI’15).
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