Stephan Tobies

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Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar. I would not have been able to write this thesis without the help of my family. I would like to thank my wife Antje, who gave me love and support; my parents, on whose assistance I could always count throughout the years; my sister, who didn't stop nagging me about(More)
While there has been a great deal of work on the development of reasoning algorithms for expressive description logics, in most cases only Tbox reasoning is considered. In this paper we present an algorithm for combined Tbox and Abox reasoning in the SHIQ description logic. This algorithm is of particular interest as it can be used to decide the problem of(More)
VCC is an industrial-strength verification environment for low-level concurrent system code written in C. VCC takes a program (annotated with function contracts, state assertions, and type invariants) and attempts to prove the correctness of these annotations. It includes tools for monitoring proof attempts and constructing partial counterexample executions(More)
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with(More)
We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C, the two variable fragment of predicate logic with counting quanti ers, which yields decidability in NExpTime. We show that this approach leads(More)
We present a PSPACE algorithm that decides satisfiability of the graded modal logic Gr(KR)—a natural extension of propositional modal logic KR by counting expressions—which plays an important role in the area of knowledge representation. The algorithm employs a tableaux approach and is the first known algorithm which meets the lower bound for the complexity(More)
We describe a practical method for reasoning about realistic concurrent programs. Our method allows global two-state invariants that restrict update of shared state. We provide simple, sufficient conditions for checking those global invariants modularly. The method has been implemented in VCC, an automatic, sound, modular verifier for concurrent C programs.(More)
When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively inexpressive logics, and it is essential to deal with such axioms in an efficient manner if implemented systems are to be(More)
ALCNIR+—ALCN augmented with transitive and inverse roles—is an expressive Description Logic which is especially well-suited for the representation of complex, aggregated objects. Despite its expressiveness, it has been conjectured that concept satisfiability for this logic could be decided in a comparatively efficient way. In this paper we prove the(More)