BeSpaceD: Towards a Tool Framework and Methodology for the Specification and Verification of Spatial Behavior of Distributed Software Component Systems

In this report, we present work towards a framework for modeling and checking behavior of spatially distributed component systems. Design goals of our framework are the ability to model spatial behavior in a component oriented, simple and intuitive way, the possibility to automatically analyse and verify systems and integration possibilities with other modeling and verification tools. We present examples and the verification steps necessary to prove properties such as range coverage or the absence of collisions between components and technical details

Initial Limit Datalog:a new extensible class of decidable constrained Horn clauses

We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types) of the first-order language limit Datalog Z (a fragment of Datalog modulo linear integer arithmetic), but can be instantiated with any suitable background theory. For example, the fragment is decidable over any countable well-quasi-order with a decidable first-order theory, such as natural number vectors under componentwise linear arithmetic, and words of a bounded, context-free language ordered by the subword relation. Formulas of initial limit Datalog have the property that, under some assumptions on the background theory, their satisfiability can be witnessed by a new kind of term model which we call entwined structures. Whilst the set of all models is typically uncountable, the set of all entwined structures is recursively enumerable, and model checking is decidable

Multiple Congruence Relations, First-Order Theories on Terms, and the Frames of the Applied Pi-Calculus

International audienceWe investigate the problem of deciding first-order theories of finite trees with several distinguished congruence relations, each of them given by some equational axioms. We give an automata-based solution for the case where the different equational axiom systems are linear and variable-disjoint (this includes the case where all axioms are ground), and where the logic does not permit to express tree relations x=f(y,z). We show that the problem is undecidable when these restrictions are relaxed. As motivation and application, we show how to translate the model-checking problem of Apil, a spatial equational logic for the applied pi-calculus, to the validity of first-order formulas in term algebras with multiple congruence relations

Saturation-based decision procedures for extensions of the guarded fragment

We apply the framework of Bachmair and Ganzinger for saturation-based theorem proving to derive a range of decision procedures for logical formalisms, starting with a simple terminological language EL, which allows for conjunction and existential restrictions only, and ending with extensions of the guarded fragment with equality, constants, functionality, number restrictions and compositional axioms of form S ◦ T ⊆ H. Our procedures are derived in a uniform way using standard saturation-based calculi enhanced with simplification rules based on the general notion of redundancy. We argue that such decision procedures can be applied for reasoning in expressive description logics, where they have certain advantages over traditionally used tableau procedures, such as optimal worst-case complexity and direct correctness proofs.Wir wenden das Framework von Bachmair und Ganzinger für saturierungsbasiertes Theorembeweisen an, um eine Reihe von Entscheidungsverfahren für logische Formalismen abzuleiten, angefangen von einer simplen terminologischen Sprache EL, die nur Konjunktionen und existentielle Restriktionen erlaubt, bis zu Erweiterungen des Guarded Fragment mit Gleichheit, Konstanten, Funktionalität, Zahlenrestriktionen und Kompositionsaxiomen der Form S ◦ T ⊆ H. Unsere Verfahren sind einheitlich abgeleitet unter Benutzung herkömmlicher saturierungsbasierter Kalküle, verbessert durch Simplifikationsregeln, die auf dem Konzept der Redundanz basieren. Wir argumentieren, daß solche Entscheidungsprozeduren für das Beweisen in ausdrucksvollen Beschreibungslogiken angewendet werden können, wo sie gewisse Vorteile gegenüber traditionell benutzten Tableauverfahren besitzen, wie z.B. optimale worst-case Komplexität und direkte Korrektheitsbeweise