A Tree Logic with Graded Paths and Nominals

Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node cardinality constraints occur along a path in a tree. We present a logic capable of expressing deep counting along paths which may include arbitrary recursive forward and backward navigation. The counting extensions can be seen as a generalization of graded modalities that count immediate successor nodes. While the combination of graded modalities, nominals, and inverse modalities yields undecidable logics over graphs, we show that these features can be combined in a tree logic decidable in exponential time

Reasoning over Ontologies with Hidden Content: The Import-by-Query Approach

There is currently a growing interest in techniques for hiding parts of the signature of an ontology Kh that is being reused by another ontology Kv. Towards this goal, in this paper we propose the import-by-query framework, which makes the content of Kh accessible through a limited query interface. If Kv reuses the symbols from Kh in a certain restricted way, one can reason over Kv U Kh by accessing only Kv and the query interface. We map out the landscape of the import-by-query problem. In particular, we outline the limitations of our framework and prove that certain restrictions on the expressivity of Kh and the way in which Kv reuses symbols from Kh are strictly necessary to enable reasoning in our setting. We also identify cases in which reasoning is possible and we present suitable import-by-query reasoning algorithms

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

Supporting Format Migration with Ontology Model Comparison

Die ausschließliche Bewahrung der reinen Bitfolge eines digitalen Dokuments führt nicht dazu, dass zu einem späteren Zeitpunkt auch Information aus dem Dokument extrahiert werden kann. Wenn keine Formatinformation verfügbar ist, muss der Inhalt des Dokuments stattdessen als verloren angesehen werden. Eine Lösung für das Problem ist die (wiederholte) Konvertierung in immer neuere Formate. Entsprechende Verfahren, diese Konvertierungen zu ermöglichen und zu automatisieren sind Teil der aktuellen Forschung. Diese Arbeit geht von der Annahme aus, dass digitale Dokumente als formale Ontologien repräsentiert werden können, was es wiederum ermöglicht, existierende Verfahren aus dem Ontology Matching zu verwenden, um Dokumentenformate aufeinander abzubilden. Bis auf wenige Ausnahmen sind existierende Verfahren beschränkt: Sie bilden Klassen auf Klassen, Rollen auf Rollen und Individuen auf Individuen ab. Solche einfachen Abbildungen sind für komplexe Dokumentenformate unzureichend. In dieser Arbeit wird zum einen eine Methode entwickelt, um einfache Abbildungen heuristisch zu komplexeren Regeln zu verfeinern. Das neue Verfahren basiert auf Tableau-Verfahren für Beschreibungslogiken und verwendet eine modelbasierte Repräsentation von komplexen Korrespondenzen. Ein zweiter Teil verwendet die modelbasierte Darstellung, um Vorschläge für bestmögliche Abbildungen zwischen Dokumenten zu finden. Die hier entwickelte Methode verwendet die semantischen Information sowohl aus dem Tableau- wie auch aus dem Verfeinerungsverfahren. Das Ergebnis ist eine neuartige Methode zur halbautomatischen Ableitung komplexer Abbildungen zwischen beschreibungslogischen Ontologien. Das Verfahren ist zugeschnitten aber nicht beschränkt auf das Feld der Formatmigration.Being able to read successfully the bits and bytes stored inside a digital archive does not necessarily mean we are able to extract meaningful information from an archived digital document. If information about the format of a stored document is not available, the contents of the document are essentially lost. One solution to the problem is format conversion, but due to the amount of documents and formats involved, manual conversion of archived documents is usually impractical. There is thus an open research question to discover suitable technologies to transform existing documents into new document formats and to determine the constraints within which these technologies can be applied successfully. In the present work, it is assumed that stored documents are represented as formal description logic ontologies. This makes it possible to view the translation of document formats as an application of ontology matching, an area for which many methods and algorithms have been developed over the recent years. With very few exceptions, however, current ontology matchers are limited to element-level correspondences matching concepts against concepts, roles against roles, and individuals against individuals. Such simple correspondences are insufficient to describe mappings between complex digital documents. This thesis presents a method to refine simple correspondences into more complex ones in a heuristic fashion utilizing a modified form of description logic tableau reasoning. The refinement process uses a model-based representation of correspondences. Building on the formal semantics, the process also includes methods to avoid the generation of inconsistent or incoherent correspondences. In a second part, this thesis also makes use of the model-based representation to determine the best set of correspondences between two ontologies. The developed similarity measures make use of semantic information from both description logic tableau reasoning as well as from the refinement process. The result is a new method to semi-automatically derive complex correspondences between description logic ontologies tailored but not limited to the context of format migration

Parallelizing Description Logic Reasoning

Description Logic has become one of the primary knowledge representation and reasoning methodologies during the last twenty years. A lot of areas are benefiting from description logic based technologies. Description logic reasoning algorithms and a number of optimization techniques for them play an important role and have been intensively researched. However, few of them have been systematically investigated in a concurrency context in spite of multi-processor computing facilities growing up. Meanwhile, semantic web, an application domain of description logic, is producing vast knowledge data on the Internet, which needs to be dealt with by using scalable solutions. This situation requires description logic reasoners to be endowed with reasoning scalability. This research introduced concurrent computing in two aspects: classification, and tableau-based description logic reasoning. Classification is a core description logic reasoning service. Over more than two decades many research efforts have been devoted to optimizing classification. Those classification optimization algorithms have shown their pragmatic effectiveness for sequential processing. However, as concurrent computing becomes widely available, new classification algorithms that are well suited to parallelization need to be developed. This need is further supported by the observation that most available OWL reasoners, which are usually based on tableau reasoning, can only utilize a single processor. Such an inadequacy often leads users working in ontology development to frustration, especially if their ontologies are complex and require long processing times. Classification service finds out all named concept subsumption relationships entailed in a knowledge base. Each subsumption test enrolls two concepts and is independent of the others. At most n^2 subsumption tests are needed for a knowledge base which contains n concepts. As the first contribution of this research, we developed an algorithm and a corresponding architecture showing that reasoning scalability can be gained by using concurrent computing. Further, this research investigated how concurrent computing can increase performance of tableau-based description logic reasoning algorithms. Tableau-based description logic reasoning decides a problem by constructing an AND-OR tree. Before this research, some research has shown the effectiveness of parallelizing processing disjunction branches of a tableau expansion tree. Our research has shown how reasoning scalability can be gained by processing conjunction branches of a tableau expansion tree. In addition, this research developed an algorithm, merge classification, that uses a divide and conquer strategy for parallelizing classification. This method applies concurrent computing to the more efficient classification algorithm, top-search & bottom-search, which has been adopted as a standard procedure for classification. Reasoning scalability can be observed in a number of real world cases by using this algorithm

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Modal satisfiability via SMT solving

Modal logics extend classical propositional logic, and they are robustly decidable. Whereas most existing decision procedures for modal logics are based on tableau constructions, we propose a framework for obtaining decision procedures by adding instantiation rules to standard SAT and SMT solvers. Soundness, completeness, and termination of the procedures can be proved in a uniform and elementary way for the basic modal logic and some extensions.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Fontaine, Pascal. Université de Lorraine; Francia.Fil: Fontaine, Pascal. National Institute for Research in Digital Science and Technology; Francia.Fil: Merz, Stephan. Université de Lorraine; Francia.Fil: Merz, Stephan. National Institute for Research in Digital Science and Technology; Francia.Ciencias de la Computació