Description Logics with Concrete Domains and Functional Dependencies

Description Logics (DLs) with concrete domains are a useful tool in many applications. To further enhance the expressive power of such DLs, it has been proposed to add database-style key constraints. Up to now, however, only uniqueness constraints have been considered in this context, thus neglecting the second fundamental family of key constraints: functional dependencies. In this paper, we consider the basic DL with concrete domains ALC(D), extend it with functional dependencies, and analyze the impact of this extension on the decidability and complexity of reasoning. Though intuitively the expressivity of functional dependencies seems weaker than that of uniqueness constraints, we are able to show that the former have a similarly severe impact on the computational properties: reasoning is undecidable in the general case, and NExpTime-complete in some slightly restricted variants of our logic

Temporal Conjunctive Queries in Expressive DLs with Non-simple Roles

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)

Query Answering in Probabilistic Data and Knowledge Bases

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

Predicate Diagrams as Basis for the Verification of Reactive Systems

This thesis proposes a diagram-based formalism for verifying temporal properties of reactive systems. Diagrams integrate deductive and algorithmic verification techniques for the verification of finite and infinite-state systems, thus combining the expressive power and flexibility of deduction with the automation provided by algorithmic methods. Our formal framework for the specification and verification of reactive systems includes the Generalized Temporal Logic of Actions (TLA*) from Merz for both mathematical modeling reactive systems and specifying temporal properties to be verified. As verification method we adopt a class of diagrams, the so-called predicate diagrams from Cansell et al. We show that the concept of predicate diagrams can be used to verify not only discrete systems, but also some more complex classes of reactive systems such as real-time systems and parameterized systems. We define two variants of predicate diagrams, namely timed predicate diagrams and parameterized predicate diagrams, which can be used to verify real-time and parameterized systems. We prove the completeness of predicate diagrams and study an approach for the generation of predicate diagrams. We develop prototype tools that can be used for supporting the generation of diagrams semi-automatically.In dieser Arbeit schlagen wir einen diagramm-basierten Formalismus für die Verifikation reaktiver Systeme vor. Diagramme integrieren die deduktiven und algorithmischen Techniken zur Verifikation endlicher und unendlicher Systeme, dadurch kombinieren sie die Ausdrucksstärke und die Flexibilität von Deduktion mit der von algoritmischen Methoden unterstützten Automatisierung. Unser Ansatz für Spezifikation und Verifikation reaktiver Systeme schließt die Generalized Temporal Logic of Actions (TLA*) von Merz ein, die für die mathematische Modellierung sowohl reaktiver Systeme als auch ihrer Eigenschaften benutzt wird. Als Methode zur Verifikation wenden wir Prädikaten-diagramme von Cansell et al. an. Wir zeigen, daß das Konzept von Prädikatendiagrammen verwendet werden kann, um nicht nur diskrete Systeme zu verifizieren, sondern auch kompliziertere Klassen von reaktiven Systemen wie Realzeitsysteme und parametrisierte Systeme. Wir definieren zwei Varianten von Prädikatendiagrammen, nämlich gezeitete Prädikatendiagramme und parametrisierte Prädikatendiagramme, die benutzt werden können, um die Realzeit- und parametrisierten Systeme zu verifizieren. Die Vollständigkeit der Prädikatendiagramme wird nachgewiesen und ein Ansatz für die Generierung von Prädikatendiagrammen wird studiert. Wir entwickeln prototypische Werkzeuge, die die semi-automatische Generierung von Diagrammen unterstützen