Efficient First-Order Temporal Logic for Infinite-State Systems

In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for this form of specification and tractable enough for practical deductive verification. Importantly, the power of the temporal language allows us to describe (and verify) asynchronous systems, communication delays and more complex properties such as liveness and fairness properties. These aspects appear difficult for many other approaches to infinite-state verification.Comment: 16 pages, 2 figure

Verification of qualitative Z\mathbb{Z} constraints

International audienceWe introduce an LTL-like logic with atomic formulae built over a constraint language interpreting variables in $\mathbb{Z}$. The constraint language includes periodicity constraints, comparison constraints of the form $x = y$ and $x < y$, it is closed under Boolean operations and it admits a restricted form of existential quantification. This is the largest set of qualitative constraints over $\mathbb{Z}$ known so far, shown to admit a decidable LTL extension. Such constraints are those used for instance in calendar formalisms or in abstractions of counter automata by using congruences modulo some power of two. Indeed, various programming languages perform arithmetic operators modulo some integer. We show that the satisfiability and model-checking problems (with respect to an appropriate class of constraint automata) for this logic are decidable in polynomial space improving significantly known results about its strict fragments. As a by-product, LTL model-checking over integral relational automata is proved complete for polynomial space which contrasts with the known undecidability of its CTL counterpart

Output constraints in multimedia database systems

Zusammenfassung Semantische Fehler treten bei jeder Art von Datenverwaltung auf. Herkömmliche Datenbanksysteme verwenden eine Integritätskontrolle, um semantische Fehler zu vermeiden. Um die Integrität der Daten zu gewährleisten werden Integritätsregeln benutzt. Diese Regeln können allerdings nur die Konsistenz einfach strukturierter Daten überprüfen. Multimedia Datenbanksystem verwalten neben einfachen alphanumerischen Daten auch komplexe Mediendaten wie Videos. Um die Konsistenz dieser Daten zu sichern, bedarf es einer erheblichen Erweiterung des bestehenden Integritätskonzeptes. Dabei muss besonders auf die konsistente Datenausgabe geachtet werden. Im Gegensatz zu alphanumerischen Daten können Mediendaten während der Ausgabe verfälscht werden. Dieser Fall kann eintreten, wenn eine geforderte Datenqualität bei der Ausgabe nicht erreicht werden kann oder wenn Synchronisationsbedingungen zwischen Medienobjekten nicht eingehalten werden können. Es besteht daher die Notwendigkeit, Ouptut Constraints einzuführen. Mit ihrer Hilfe kann definiert werden, wann die Ausgabe von Mediendaten semantisch korrekt ist. Das Datenbanksystem kann diese Bedingungen überprüfen und so gewährleisten, dass der Nutzer semantisch einwandfreie Daten erhält. In dieser Arbeit werden alle Aspekte betrachtet, die notwendig sind, um Ausgabebedingungen in ein Multimedia Datenbanksystem zu integrieren. Im einzelnen werden die Modellierung der Bedingungen, deren datenbankinterne Repräsentation sowie die Bedingungsüberprüfung betrachtet. Für die Bedingungsmodellierung wird eine Constraint Language auf Basis der Prädikatenlogik eingeführt. Um die Definition von zeitlichen und räumlichen Synchronisationen zu ermöglichen, verwenden wir Allen-Relationen. Für die effiziente Überprüfung der Ausgabebedingungen müssen diese aus der Spezifikationssprache in eine datenbankinterne Darstellung überführt werden. Für die datenbankinterne Darstellung werden Difference Constraints verwendet. Diese erlauben eine sehr effiziente Bedingungsüberprüfung. Wir haben Algorithmen entwickelt, die eine effiziente Überprüfung von Ausgabebedingungen erlauben und dies anhand von Experimenten nachgewiesen. Neben der Überprüfung der Bedingungen müssen Mediendaten so synchronisiert werden, dass dies den Ausgabebedingungen entspricht. Wir haben dazu das Konzept des Output Schedules entwickelt. Dieser wird aufgrund der definierten Ausgabebedingungen generiert. Durch die Ausgabebedingungen, die in dieser Arbeit eingeführt werden, werden semantische Fehler bei der Verwaltung von Mediendaten erheblich reduziert. Die Arbeit stellt daher einen Beitrag zur qualitativen Verbesserung der Verwaltung von Mediendaten dar.Semantic errors exist as long as data are managed. Traditional database systems try to prevent this errors by proposing integrity concepts for stored data. Integrity constraints are used to implement these integrity concepts. However, integrity constraints can only detect semantic errors in elementary data. Multimedia database systems manage elementary data as well as complex media data, like videos. Considering these media data we need a much wider consistency concept as traditional database systems provide. Especially, data output of media data must be taken into account. In contrast to alphanumeric data the semantics of media data can be falsified during data output if data quality or synchronization of data are not suitable. Thus, we need a concept for output constraints that allow for preventing semantic errors in case of data output. For integrating output constraints into a multimedia database system we have to consider modelling, representation and checking of output constraints. For modelling output constraints we have introduced a constraint language which uses the same principles as traditional constraint languages. Our constraint specification language must support temporal and spatial synchronization constraints. However, it is desired to support both kinds of synchronization in almost the same manner. Therefore, we use Allen-Relations for defining temporal synchronization constraints as well as for defining spatial synchronization constraints. We need a database internal representation of output constraints that makes efficient constraint checking possible. The Allen-Relations used in the constraint language cannot be checked efficiently. However, difference constraints are a class of constraints that allows an very efficient checking. Therefore, we use difference constraints as database internal representation of output constraints. As methods for checking consistency of output constraints we use an approach based on graph theory as well as an analytical approach. Both approaches require a constraint graph as data structure. For data output we need an output order that is adequate to the defined output constraints. This output schedule can be produced based on the output constraints. With output constraints, proposed in this thesis, semantical correctness of media data considering the data output can be supported.Thus, the contribution of this work is an qualitative improvement of managing media data by database systems

Declarative Reasoning about Moving Objects

There are numerous applications where there is a critical need to reason about moving object plans under uncertainty. Previous work on spatio-temporal logics is limited to qualitative approaches and the work on spatio-temporal databases focus on the observations ignoring the intended movements of the objects. This thesis presents a Logic of Motion (LOM), a novel theory and algorithms that combine logic, constraint satisfaction and geometric reasoning. LOM provides a declarative syntax and model theory and formalizes how to reason about planned movements of objects, when there is uncertainty. LOM is the first quantitative logical treatment of moving objects that can account for the fact that we are not always sure when an object will leave or arrive a given location, and what its velocity will be. The thesis includes the following contributions: 1) LOM, the first quantitative logic to reason about flexible plans for moving objects. 2) An analysis of the computational complexity of reasoning with flexible plans for moving objects. This analysis includes an important theoretical result showing that complexity of consistency checking for LOM theories is at least NP-hard. I also provide algorithms to check consistency of a fraction of LOM theories called go-theories. 3) A class of motion theories, called Simple Go-Theories that are tractable. 4) Efficient algorithms to answer ground and non-ground queries in LOM concerning the possible location of the object and its proximity to other objects. 5) A study of default reasoning for motion-theories. It presents a motion closed world assumption for LOM that restrict the reasoning within a class of preferred models of the theory. Motion closed world assumption allows us to make more intelligent and customized inferences. 6) An investigation of deconfliction of motion-theories with respect to some integrity constraints. A deconfliction of a theory is a modification to the theory such that any model of the modified theory will entail the integrity constraints. I present an algorithm for efficiently computing a deconfliction of a theory. 7) Extensive empirical evaluation to demonstrate the efficiency of consistency checking, query answering and deconfliction algorithms

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 &#9702; T &#8838; 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 &#9702; T &#8838; 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

On the computational complexity of spatio-temporal logics

Recently, a hierarchy of spatio-temporal languages based on the propositional temporal logic PTL and the spatial languages RCC-8, BRCC-8 and S4u has been introduced. Although a number of results on their computational properties were obtained, the most important questions were left open. In this paper, we solve these problems and provide a clear picture of the balance between expressiveness and "computational realisability" within the hierarchy