Proceedings of Sixth International Workshop on Unification

Swiss National Science Foundation; Austrian Federal Ministry of Science and Research; Deutsche Forschungsgemeinschaft (SFB 314); Christ Church, Oxford; Oxford University Computing Laborator

Hierarchical Combination of Unification Algorithms

International audienceA critical question in unification theory is how to obtain a unification algorithm for the combination of non-disjoint equational theories when there exists unification algorithms for the constituent theories. The problem is known to be difficult and can easily be seen to be undecidable in the general case. Therefore, previous work has focused on identifying specific conditions and methods in which the problem is decidable. We continue the investigation in this paper, building on previous combination results. We are able to develop a novel approach to the non-disjoint combination problem. The approach is based on a new set of restrictions and combination method such that if the restrictions are satisfied the method produces an algorithm for the unification problem in the union of non-disjoint equational theories

Combining Decision Algorithms for Matching in the Union of Disjoint Equational Theories

AbstractThis paper addresses the problem of systematically building a matching algorithm for the union of two disjoint theoriesE1∪E2provided that matching algorithms are known in both theoriesE1andE2. In general, the blind use of combination techniques introduces unification. Two different restrictions are considered in order to reduce this unification to matching. First, we show that combining matching algorithms (with linear constant restriction) is always sufficient for solving a pure fragment of combined matching problems. Second, the investigated method is complete for the largest class of theories where unification is not needed, including regular collapse-free theories and linear theories. Syntactic conditions are given to define this class of theories in which solving the combined matching problem is performed in a modular way

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

A class of theory-decidable inference systems

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2004-2005Dans les deux dernières décennies, l’Internet a apporté une nouvelle dimension aux communications. Il est maintenant possible de communiquer avec n’importe qui, n’importe où, n’importe quand et ce, en quelques secondes. Alors que certains systèmes de communication distribués, comme le courriel, le chat, . . . , sont plutôt informels et ne nécessitent aucune sécurité, d’autres comme l’échange d’informations militaires ou encore médicales, le commerce électronique, . . . , sont très formels et nécessitent de très hauts niveaux de sécurité. Pour atteindre les objectifs de sécurité voulus, les protocoles cryptographiques sont souvent utilisés. Cependant, la création et l’analyse de ces protocoles sont très difficiles. Certains protocoles ont été montrés incorrects plusieurs années après leur conception. Nous savons maintenant que les méthodes formelles sont le seul espoir pour avoir des protocoles parfaitement corrects. Ce travail est une contribution dans le domaine de l’analyse des protocoles cryptographiques de la façon suivante: • Une classification des méthodes formelles utilisées pour l’analyse des protocoles cryptographiques. • L’utilisation des systèmes d’inférence pour la mod´elisation des protocoles cryptographiques. • La définition d’une classe de systèmes d’inférence qui ont une theorie décidable. • La proposition d’une procédure de décision pour une grande classe de protocoles cryptographiquesIn the last two decades, Internet brought a new dimension to communications. It is now possible to communicate with anyone, anywhere at anytime in few seconds. While some distributed communications, like e-mail, chat, . . . , are rather informal and require no security at all, others, like military or medical information exchange, electronic-commerce, . . . , are highly formal and require a quite strong security. To achieve security goals in distributed communications, it is common to use cryptographic protocols. However, the informal design and analysis of such protocols are error-prone. Some protocols were shown to be deficient many years after their conception. It is now well known that formal methods are the only hope of designing completely secure cryptographic protocols. This thesis is a contribution in the field of cryptographic protocols analysis in the following way: • A classification of the formal methods used in cryptographic protocols analysis. • The use of inference systems to model cryptographic protocols. • The definition of a class of theory-decidable inference systems. • The proposition of a decision procedure for a wide class of cryptographic protocols

Assertion level proof planning with compiled strategies

This book presents new techniques that allow the automatic verification and generation of abstract human-style proofs. The core of this approach builds an efficient calculus that works directly by applying definitions, theorems, and axioms, which reduces the size of the underlying proof object by a factor of ten. The calculus is extended by the deep inference paradigm which allows the application of inference rules at arbitrary depth inside logical expressions and provides new proofs that are exponentially shorter and not available in the sequent calculus without cut. In addition, a strategy language for abstract underspecified declarative proof patterns is developed. Together, the complementary methods provide a framework to automate declarative proofs. The benefits of the techniques are illustrated by practical applications.Die vorliegende Arbeit beschäftigt sich damit, das Formalisieren von Beweisen zu vereinfachen, indem Methoden entwickelt werden, um informale Beweise formal zu verifizieren und erzeugen zu können. Dazu wird ein abstrakter Kalkül entwickelt, der direkt auf der Faktenebene arbeitet, welche von Menschen geführten Beweisen relativ nahe kommt. Anhand einer Fallstudie wird gezeigt, dass die abstrakte Beweisführung auf der Fakteneben vorteilhaft für automatische Suchverfahren ist. Zusätzlich wird eine Strategiesprache entwickelt, die es erlaubt, unterspezifizierte Beweismuster innerhalb des Beweisdokumentes zu spezifizieren und Beweisskizzen automatisch zu verfeinern. Fallstudien zeigen, dass komplexe Beweismuster kompakt in der entwickelten Strategiesprache spezifiziert werden können. Zusammen bilden die einander ergänzenden Methoden den Rahmen zur Automatisierung von deklarativen Beweisen auf der Faktenebene, die bisher überwiegend manuell entwickelt werden mussten

Assertion level proof planning with compiled strategies

This book presents new techniques that allow the automatic verification and generation of abstract human-style proofs. The core of this approach builds an efficient calculus that works directly by applying definitions, theorems, and axioms, which reduces the size of the underlying proof object by a factor of ten. The calculus is extended by the deep inference paradigm which allows the application of inference rules at arbitrary depth inside logical expressions and provides new proofs that are exponentially shorter and not available in the sequent calculus without cut. In addition, a strategy language for abstract underspecified declarative proof patterns is developed. Together, the complementary methods provide a framework to automate declarative proofs. The benefits of the techniques are illustrated by practical applications.Die vorliegende Arbeit beschäftigt sich damit, das Formalisieren von Beweisen zu vereinfachen, indem Methoden entwickelt werden, um informale Beweise formal zu verifizieren und erzeugen zu können. Dazu wird ein abstrakter Kalkül entwickelt, der direkt auf der Faktenebene arbeitet, welche von Menschen geführten Beweisen relativ nahe kommt. Anhand einer Fallstudie wird gezeigt, dass die abstrakte Beweisführung auf der Fakteneben vorteilhaft für automatische Suchverfahren ist. Zusätzlich wird eine Strategiesprache entwickelt, die es erlaubt, unterspezifizierte Beweismuster innerhalb des Beweisdokumentes zu spezifizieren und Beweisskizzen automatisch zu verfeinern. Fallstudien zeigen, dass komplexe Beweismuster kompakt in der entwickelten Strategiesprache spezifiziert werden können. Zusammen bilden die einander ergänzenden Methoden den Rahmen zur Automatisierung von deklarativen Beweisen auf der Faktenebene, die bisher überwiegend manuell entwickelt werden mussten