Knowledge Problems in Security Protocols: Going Beyond Subterm Convergent Theories

We introduce a new form of restricted term rewrite system, the graph-embedded term rewrite system. These systems, and thus the name, are inspired by the graph minor relation and are more flexible extensions of the well-known homeomorphic-embedded property of term rewrite systems. As a motivating application area, we consider the symbolic analysis of security protocols, and more precisely the two knowledge problems defined by the deduction problem and the static equivalence problem. In this field restricted term rewrite systems, such as subterm convergent ones, have proven useful since the knowledge problems are decidable for such systems. However, many of the same decision procedures still work for examples of systems which are "beyond subterm convergent". However, the applicability of the corresponding decision procedures to these examples must often be proven on an individual basis. This is due to the problem that they don\u27t fit into an existing syntactic definition for which the procedures are known to work. Here we show that many of these systems belong to a particular subclass of graph-embedded convergent systems, called contracting convergent systems. On the one hand, we show that the knowledge problems are decidable for the subclass of contracting convergent systems. On the other hand, we show that the knowledge problems are undecidable for the class of graph-embedded systems

Intuitionistic S4 is decidable

In this paper we demonstrate decidability for the intuitionistic modal logic S4 first formulated by Fischer Servi. This solves a problem that has been open for almost thirty years since it had been posed in Simpson's PhD thesis in 1994. We obtain this result by performing proof search in a labelled deductive system that, instead of using only one binary relation on the labels, employs two: one corresponding to the accessibility relation of modal logic and the other corresponding to the order relation of intuitionistic Kripke frames. Our search algorithm outputs either a proof or a finite counter-model, thus, additionally establishing the finite model property for intuitionistic S4, which has been another long-standing open problem in the area.Comment: 13 pages conference paper + 26 pages appendix with examples and proof

The Dynamic Creation of Induction Rules Using Proof Planning

Centre for Intelligent Systems and their ApplicationsA key problem in automating proof by mathematical induction is choosing an induction rule suitable for a given conjecture. Since Boyer & Moore’s NQTHM system the standard approach has been based on recursion analysis, which uses a combination of induction rules based on the relevant recursive function definitions. However, there are practical examples on which such techniques are known to fail. Recent research has tried to improve automation by delaying the choice of inductive rule until later in the proof, but these techniques suffer from two serious problems. Firstly, a lack of search control: specifically, in controlling the application of ‘speculative’ proof steps that partially commit to a choice of induction rule. Secondly, a lack of generality: they place significant restrictions on the form of induction rule that can be chosen. In this thesis we describe a new delayed commitment strategy for inductive proof that addresses these problems. The strategy dynamically creates an appropriate induction rule by proving schematic proof goals, where unknown rule structure is represented by meta-variables which become instantiated during the proof. This is accompanied by a proof that the generated rule is valid. The strategy achieves improved control over speculative proof steps via a novel speculation critic. It also generates a wider range of useful induction rules than other delayed commitment techniques, partly because it removes unnecessary restrictions on the individual proof cases, and partly because of a new technique for generating the rule’s overall case structure. The basic version of the strategy has been implemented using the lamdaClam proof planner. The system was extended with a novel proof critics architecture for this purpose. An evaluation shows the strategy is a useful and practical technique, and demonstrates its advantages

Explainable methods for knowledge graph refinement and exploration via symbolic reasoning

Knowledge Graphs (KGs) have applications in many domains such as Finance, Manufacturing, and Healthcare. While recent efforts have created large KGs, their content is far from complete and sometimes includes invalid statements. Therefore, it is crucial to refine the constructed KGs to enhance their coverage and accuracy via KG completion and KG validation. It is also vital to provide human-comprehensible explanations for such refinements, so that humans have trust in the KG quality. Enabling KG exploration, by search and browsing, is also essential for users to understand the KG value and limitations towards down-stream applications. However, the large size of KGs makes KG exploration very challenging. While the type taxonomy of KGs is a useful asset along these lines, it remains insufficient for deep exploration. In this dissertation we tackle the aforementioned challenges of KG refinement and KG exploration by combining logical reasoning over the KG with other techniques such as KG embedding models and text mining. Through such combination, we introduce methods that provide human-understandable output. Concretely, we introduce methods to tackle KG incompleteness by learning exception-aware rules over the existing KG. Learned rules are then used in inferring missing links in the KG accurately. Furthermore, we propose a framework for constructing human-comprehensible explanations for candidate facts from both KG and text. Extracted explanations are used to insure the validity of KG facts. Finally, to facilitate KG exploration, we introduce a method that combines KG embeddings with rule mining to compute informative entity clusters with explanations.Wissensgraphen haben viele Anwendungen in verschiedenen Bereichen, beispielsweise im Finanz- und Gesundheitswesen. Wissensgraphen sind jedoch unvollständig und enthalten auch ungültige Daten. Hohe Abdeckung und Korrektheit erfordern neue Methoden zur Wissensgraph-Erweiterung und Wissensgraph-Validierung. Beide Aufgaben zusammen werden als Wissensgraph-Verfeinerung bezeichnet. Ein wichtiger Aspekt dabei ist die Erklärbarkeit und Verständlichkeit von Wissensgraphinhalten für Nutzer. In Anwendungen ist darüber hinaus die nutzerseitige Exploration von Wissensgraphen von besonderer Bedeutung. Suchen und Navigieren im Graph hilft dem Anwender, die Wissensinhalte und ihre Limitationen besser zu verstehen. Aufgrund der riesigen Menge an vorhandenen Entitäten und Fakten ist die Wissensgraphen-Exploration eine Herausforderung. Taxonomische Typsystem helfen dabei, sind jedoch für tiefergehende Exploration nicht ausreichend. Diese Dissertation adressiert die Herausforderungen der Wissensgraph-Verfeinerung und der Wissensgraph-Exploration durch algorithmische Inferenz über dem Wissensgraph. Sie erweitert logisches Schlussfolgern und kombiniert es mit anderen Methoden, insbesondere mit neuronalen Wissensgraph-Einbettungen und mit Text-Mining. Diese neuen Methoden liefern Ausgaben mit Erklärungen für Nutzer. Die Dissertation umfasst folgende Beiträge: Insbesondere leistet die Dissertation folgende Beiträge: • Zur Wissensgraph-Erweiterung präsentieren wir ExRuL, eine Methode zur Revision von Horn-Regeln durch Hinzufügen von Ausnahmebedingungen zum Rumpf der Regeln. Die erweiterten Regeln können neue Fakten inferieren und somit Lücken im Wissensgraphen schließen. Experimente mit großen Wissensgraphen zeigen, dass diese Methode Fehler in abgeleiteten Fakten erheblich reduziert und nutzerfreundliche Erklärungen liefert. • Mit RuLES stellen wir eine Methode zum Lernen von Regeln vor, die auf probabilistischen Repräsentationen für fehlende Fakten basiert. Das Verfahren erweitert iterativ die aus einem Wissensgraphen induzierten Regeln, indem es neuronale Wissensgraph-Einbettungen mit Informationen aus Textkorpora kombiniert. Bei der Regelgenerierung werden neue Metriken für die Regelqualität verwendet. Experimente zeigen, dass RuLES die Qualität der gelernten Regeln und ihrer Vorhersagen erheblich verbessert. • Zur Unterstützung der Wissensgraph-Validierung wird ExFaKT vorgestellt, ein Framework zur Konstruktion von Erklärungen für Faktkandidaten. Die Methode transformiert Kandidaten mit Hilfe von Regeln in eine Menge von Aussagen, die leichter zu finden und zu validieren oder widerlegen sind. Die Ausgabe von ExFaKT ist eine Menge semantischer Evidenzen für Faktkandidaten, die aus Textkorpora und dem Wissensgraph extrahiert werden. Experimente zeigen, dass die Transformationen die Ausbeute und Qualität der entdeckten Erklärungen deutlich verbessert. Die generierten unterstützen Erklärungen unterstütze sowohl die manuelle Wissensgraph- Validierung durch Kuratoren als auch die automatische Validierung. • Zur Unterstützung der Wissensgraph-Exploration wird ExCut vorgestellt, eine Methode zur Erzeugung von informativen Entitäts-Clustern mit Erklärungen unter Verwendung von Wissensgraph-Einbettungen und automatisch induzierten Regeln. Eine Cluster-Erklärung besteht aus einer Kombination von Relationen zwischen den Entitäten, die den Cluster identifizieren. ExCut verbessert gleichzeitig die Cluster- Qualität und die Cluster-Erklärbarkeit durch iteratives Verschränken des Lernens von Einbettungen und Regeln. Experimente zeigen, dass ExCut Cluster von hoher Qualität berechnet und dass die Cluster-Erklärungen für Nutzer informativ sind

The 1st Verified Software Competition, Extended Experience Report

We, the organizers and participants, report our experiences from the 1st Veried Software Competition, held in August 2010 in Edinburgh at the VSTTE 2010 conferenc

The 1st Verified Software Competition, Extended Experience Report

We, the organizers and participants, report our experiences from the 1st Veried Software Competition, held in August 2010 in Edinburgh at the VSTTE 2010 conferenc

Deciding Piecewise Testable Separability for Regular Tree Languages

The piecewise testable separability problem asks, given two input languages, whether there exists a piecewise testable language that contains the first input language and is disjoint from the second. We prove a general characterisation of piecewise testable separability on languages in a well-quasiorder, in terms of ideals of the ordering. This subsumes the known characterisations in the case of finite words. In the case of finite ranked trees ordered by homeomorphic embedding, we show using effective representations for tree ideals that it entails the decidability of piecewise testable separability when the input languages are regular. A final byproduct is a new proof of the decidability of whether an input regular language of ranked trees is piecewise testable, which was first shown in the unranked case by Bojanczyk, Segoufin, and Straubing [Log. Meth. in Comput. Sci., 8(3:26), 2012]