A Default Logic Patch for Default Logic

International audienceThis paper is about the fusion of multiple information sources represented using default logic. More precisely, the focus is on solving the problem that occurs when the standard-logic knowledge parts of the sources are contradictory, as default theories trivialize in this case. To overcome this problem, it is shown that replacing each formula belonging to Minimally Unsatisfiable Subformulas by a corresponding supernormal default allows appealing features. Moreover, it is investigated how these additional defaults interact with the initial defaults of the theory. Interestingly, this approach allows us to handle the problem of default theories containing inconsistent standard-logic knowledge, using the default logic framework itself

Erklären von Erfüllbarkeitsanfragen für Softwareproduktlinien

Many analyses have been proposed to ensure the correctness of the various models used throughout software product line development. However, these analyses often merely serve to detect such circumstances without providing any means for dealing with them once encountered. To aid the software product line developer in understanding the cause of defects, a new algorithm capable of explaining satisfiability queries in a software product line context is presented in this thesis. This algorithm finds explanations by using SAT solvers to extract minimal unsatisfiable subsets from the propositional formulas that express the defects. The algorithm is applied to feature model defects such as dead features and redundant constraints, automatic truth value propagations in configurations, and preprocessor annotations that are superfluous or cause dead code blocks. Using feature models and configurations from real software product lines of varying sizes, this approach is evaluated against an existing explanation approach based on Boolean constraint propagation. The results show that Boolean constraint propagation occasionally fails to find any explanation at all but is magnitudes faster than using minimal unsatisfiable subset extractors. In response, both algorithms are combined into a single one that is as fast as Boolean constraint propagation for the cases where that finds an explanation, but also finds an explanation for all the other cases.Viele Analysen wurden vorgeschlagen, um die Korrektheit der verschiedenen in der Entwicklung von Softwareproduktlinien genutzten Modelle zu gewährleisten. Allerdings dienen diese Analysen häufig lediglich dem Erkennen solcher Umstände, ohne Mittel zu liefern, sie zu lösen, sobald sie angetroffen wurden. Um dem Entwickler der Softwareproduktlinie das Verstehen der Ursache der Defekte zu erleichtern, wird in dieser Arbeit ein neuer Algorithmus zum Erklären von Erfüllbarkeitsanfragen im Kontext von Softwareproduktlinien vorgestellt. Dieser Algorithmus findet Erklärungen, indem mittels SAT-Solvern eine minimale unerfüllbare Teilmenge aus der aussagenlogischen Formel, die den Defekt ausdrückt, extrahiert wird. Der Algorithmus wird angewandt auf Defekte in Feature-Modellen wie tote Features und redundante Constraints, automatische Resolution von Wahrheitswerten in Konfigurationen sowie Präprozessorannotationen, die überflüssig sind oder tote Code-Blocks verursachen. Dieser Ansatz wird anhand von Feature-Modellen und Konfigurationen aus echten Softwareproduktlinien verschiedener Größen gegen einen existierenden, auf Boolean-Constraint-Propagation basierenden Ansatz zum Erklären evaluiert. Die Ergebnisse zeigen, dass Boolean-Constraint-Propagation gelegentlich gar keine Erklärung findet, aber um Größenordnungen schneller als mittels Extraktoren für minimale unerfüllbare Teilmengen ist. Daraufhin werden beide Algorithmen in einem einzigen verbunden, der so schnell wie Boolean-Constraint-Propagation ist, wenn dieser eine Erklärung findet, aber auch eine Erklärung in allen übrigen Fällen findet

Combining Spatial and Temporal Logics: Expressiveness vs. Complexity

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and computational realisability within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete

A Constructor-Based Reachability Logic for Rewrite Theories

Reachability logic has been applied to K rewrite-rule-based language definitions as a language-generic logic of programs. It has been proved successful in verifying a wide range of sophisticated programs in conventional languages. Here we study how reachability logic can be made not just language-generic, but rewrite-theory-generic to make it available not just for conventional program verification, but also to verify rewriting-logic-based programs and distributed system designs. A theory-generic reachability logic is presented and proved sound for a wide class of rewrite theories. Particular attention is given to increasing the logic's automation by means of constructor-based semantic unification, matching, and satisfiability procedures. The relationships to Hoare logic and LTL are discussed, new methods for proving invariants of possibly never terminating distributed systems are developed, and experiments with a prototype implementation illustrating the new methods are presented.Partially supported by NSF Grants CNS 13-19109 and CNS 14-09416, and AFOSR Contract FA8750-11-2-0084.Ope