First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries

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 standard congruence predicates t \equiv 0 mod n, for any fixed n > 1, and FO(RPR) that admits relational primitive recursion. In terms of circuit complexity, FOE- and FO(RPR)-rewritability guarantee answering OMQs in uniform AC0 and NC1, respectively. We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL ontology languages and investigate the FO-rewritability of OMQs with atomic queries by constructing projections onto 1D LTL OMQs and employing recent results on the FO-rewritability of propositional LTL OMQs. As the projections involve deciding consistency of ontologies and data, we also consider the consistency problem for our languages. While the undecidability of consistency for 2D ontology languages with expressive Boolean role inclusions might be expected, we also show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to decidability (and ExpSpace-completeness), even if one admits full Booleans on concepts. As a final step, we lift some of the rewritability results for atomic OMQs to OMQs with expressive positive temporal instance queries. The lifting results are based on an in-depth study of the canonical models and only concern Horn ontologies

Xcerpt: A Rule-Based Query and Transformation Language for the Web

This thesis investigates querying the Web and the Semantic Web. It proposes a new rulebased query language called Xcerpt. Xcerpt differs from other query languages in that it uses patterns instead of paths for the selection of data, and in that it supports both rule chaining and recursion. Rule chaining serves for structuring large queries, as well as for designing complex query programs (e.g. involving queries to the Semantic Web), and for modelling inference rules. Query patterns may contain special constructs like partial subqueries, optional subqueries, or negated subqueries that account for the particularly flexible structure of data on the Web. Furthermore, this thesis introduces the syntax of the language Xcerpt, which is illustrated on a large collection of use cases both from the conventional Web and the Semantic Web. In addition, a declarative semantics in form of a Tarski-style model theory is described, and an algorithm is proposed that performs a backward chaining evaluation of Xcerpt programs. This algorithm has also been implemented (partly) in a prototypical runtime system. A salient aspect of this algorithm is the specification of a non-standard unification algorithm called simulation unification that supports the new query constructs described above. This unification is symmetric in the sense that variables in both terms can be bound. On the other hand it is in contrast to standard unification assymmetric in the sense that the unification determines that the one term is a subterm of the other term.Diese Arbeit untersucht das Anfragen des Webs und des Semantischen Webs. Sie stellt eine neue regel-basierte Anfragesprache namens Xcerpt vor. Xcerpt unterscheidet sich von anderen Anfragesprachen insofern, als dass es zur Selektion von Daten sog. Pattern (,,Muster'') verwendet und sowohl Regelschliessen als auch Rekursion unterstützt, was sowohl zur Strukturierung größerer Anfragen als auch zur Erstellung komplexer Anfrageprogramme, und zur Modellierung von Inferenzregeln dient. Anfrage-Pattern können spezielle Konstrukte, wie partielle Teilanfragen, optionale Teilanfragen, oder negierte Teilanfragen, enthalten, die der besonders flexiblen Struktur von Daten im Web genügen. In dieser Arbeit wird weiterhin die Syntax von Xcerpt eingeführt, und mit Hilfe mehrerer Anwendungsszenarien sowohl aus dem konventionellen als auch aus dem semantischen Web erläutert. Ausserdem wird eine deklarative Semantik im Stil von Tarski's Modelltheorie beschrieben und ein Algorithmus vorgeschlagen, der eine rückwärtsschliessende Auswertung von Xcerpt durchführt und in einem prototypischen Laufzeitsystem implementiert wurde. Wesentlicher Bestandteil des Rückwärtsschliessens ist die Spezifikation eines nicht-standard Unifikations-Algorithmus, der die oben genannten speziellen Xcerpt-Konstrukte berücksichtigt. Diese Unifikation ist symmetrisch in dem Sinne, dass sie Variablen in beiden angeglichenen (,,unifizierten'') Termen binden kann. Andererseits ist sie im Gegensatz zur Standardunifikation assymmetrisch in dem Sinne, dass der dadurch geleistete Angleich den einen Term als ,,Teilterm'' des anderen erkennt