Reasoning with Forest Logic Programs and f-hybrid Knowledge Bases

Open Answer Set Programming (OASP) is an undecidable framework for integrating ontologies and rules. Although several decidable fragments of OASP have been identified, few reasoning procedures exist. In this article, we provide a sound, complete, and terminating algorithm for satisfiability checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules have a tree shape and allow for inequality atoms and constants. The algorithm establishes a decidability result for FoLPs. Although believed to be decidable, so far only the decidability for two small subsets of FoLPs, local FoLPs and acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a hybrid framework where \SHOQ{} knowledge bases and forest logic programs co-exist, and we show that reasoning with such knowledge bases can be reduced to reasoning with forest logic programs only. We note that f-hybrid knowledge bases do not require the usual (weakly) DL-safety of the rule component, providing thus a genuine alternative approach to current integration approaches of ontologies and rules

Temporalised Description Logics for Monitoring Partially Observable Events

Inevitably, it becomes more and more important to verify that the systems surrounding us have certain properties. This is indeed unavoidable for safety-critical systems such as power plants and intensive-care units. We refer to the term system in a broad sense: it may be man-made (e.g. a computer system) or natural (e.g. a patient in an intensive-care unit). Whereas in Model Checking it is assumed that one has complete knowledge about the functioning of the system, we consider an open-world scenario and assume that we can only observe the behaviour of the actual running system by sensors. Such an abstract sensor could sense e.g. the blood pressure of a patient or the air traffic observed by radar. Then the observed data are preprocessed appropriately and stored in a fact base. Based on the data available in the fact base, situation-awareness tools are supposed to help the user to detect certain situations that require intervention by an expert. Such situations could be that the heart-rate of a patient is rather high while the blood pressure is low, or that a collision of two aeroplanes is about to happen. Moreover, the information in the fact base can be used by monitors to verify that the system has certain properties. It is not realistic, however, to assume that the sensors always yield a complete description of the current state of the observed system. Thus, it makes sense to assume that information that is not present in the fact base is unknown rather than false. Moreover, very often one has some knowledge about the functioning of the system. This background knowledge can be used to draw conclusions about the possible future behaviour of the system. Employing description logics (DLs) is one way to deal with these requirements. In this thesis, we tackle the sketched problem in three different contexts: (i) runtime verification using a temporalised DL, (ii) temporalised query entailment, and (iii) verification in DL-based action formalisms

Reasoning with Very Expressive Fuzzy Description Logics

It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN

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

Derivation methods for hybrid knowledge bases with rules and ontologies

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia InformáticaFirst of all, I would like to thank my advisor, José Júlio Alferes, for his incredible support. Right from the start, during the first semester of this work, when we were 2700 km apart and meeting regularly via Skype, until the end of this dissertation, he was always committed and available for discussions, even when he had lots of other urgent things to do. A really special thanks to Terrance Swift, whom acted as an advisor, helping me a lot in the second implementation, and correcting all XSB’s and CDF’s bugs. This implementation wouldn’t surely have reached such a fruitful end without his support. I would also like to thank all my colleagues and friends at FCT for the great work environment and for not letting me take myself too serious. A special thanks to my colleagues from Dresden for encouraging me to work even when there were so many other interesting things to do as an Erasmus student. I’m indebted to Luís Leal, Bárbara Soares, Jorge Soares and Cecília Calado, who kindly accepted to read a preliminary version of this report and gave me their valuable comments. For giving me working conditions and a partial financial support, I acknowledge the Departamento de Informática of the Faculdade de Ciências e Tecnologias of Universidade Nova de Lisboa. Last, but definitely not least, I would like to thank my parents and all my family for their continuous encouragement and motivation. A special thanks to Bruno for his love, support and patience

OPTIMIZATION OF NONSTANDARD REASONING SERVICES

The increasing adoption of semantic technologies and the corresponding increasing complexity of application requirements are motivating extensions to the standard reasoning paradigms and services supported by such technologies. This thesis focuses on two of such extensions: nonmonotonic reasoning and inference-proof access control. Expressing knowledge via general rules that admit exceptions is an approach that has been commonly adopted for centuries in areas such as law and science, and more recently in object-oriented programming and computer security. The experiences in developing complex biomedical knowledge bases reported in the literature show that a direct support to defeasible properties and exceptions would be of great help. On the other hand, there is ample evidence of the need for knowledge confidentiality measures. Ontology languages and Linked Open Data are increasingly being used to encode the private knowledge of companies and public organizations. Semantic Web techniques facilitate merging different sources of knowledge and extract implicit information, thereby putting at risk security and the privacy of individuals. But the same reasoning capabilities can be exploited to protect the confidentiality of knowledge. Both nonmonotonic inference and secure knowledge base access rely on nonstandard reasoning procedures. The design and realization of these algorithms in a scalable way (appropriate to the ever-increasing size of ontologies and knowledge bases) is carried out by means of a diversified range of optimization techniques such as appropriate module extraction and incremental reasoning. Extensive experimental evaluation shows the efficiency of the developed optimization techniques: (i) for the first time performance compatible with real-time reasoning is obtained for large nonmonotonic ontologies, while (ii) the secure ontology access control proves to be already compatible with practical use in the e-health application scenario.

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

Approximate Assertional Reasoning Over Expressive Ontologies

In this thesis, approximate reasoning methods for scalable assertional reasoning are provided whose computational properties can be established in a well-understood way, namely in terms of soundness and completeness, and whose quality can be analyzed in terms of statistical measurements, namely recall and precision. The basic idea of these approximate reasoning methods is to speed up reasoning by trading off the quality of reasoning results against increased speed

Dokumentverifikation mit Temporaler Beschreibungslogik

The thesis proposes a new formal framework for checking the content of web documents along individual reading paths. It is vital for the readability of web documents that their content is consistent and coherent along the possible browsing paths through the document. Manually ensuring the coherence of content along the possibly huge number of different browsing paths in a web document is time-consuming and error-prone. Existing methods for document validation and verification are not sufficiently expressive and efficient. The innovative core idea of this thesis is to combine the temporal logic CTL and description logic ALC for the representation of consistency criteria. The resulting new temporal description logics ALCCTL can - in contrast to existing specification formalisms - compactly represent coherence criteria on documents. Verification of web documents is modelled as a model checking problem of ALCCTL. The decidability and polynomial complexity of the ALCCTL model checking problem is proven and a sound, complete, and optimal model checking algorithm is presented. Case studies on real and realistic web documents demonstrate the performance and adequacy of the proposed methods. Existing methods such as symbolic model checking or XML-based document validation are outperformed in both expressiveness and speed.Die Dissertation stellt ein neues formales Framework für die automatische Prüfung inhaltlich-struktureller Konsistenzkriterien an Web-Dokumente vor. Viele Informationen werden heute in Form von Web-Dokumenten zugänglich gemacht. Komplexe Dokumente wie Lerndokumente oder technische Dokumentationen müssen dabei vielfältige Qualitätskriterien erfüllen. Der Informationsgehalt des Dokuments muss aktuell, vollständig und in sich stimmig sein. Die Präsentationsstruktur muss unterschiedlichen Zielgruppen mit unterschiedlichen Informationsbedürfnissen genügen. Die Sicherstellung grundlegender Konsistenzeigenschaften von Dokumenten ist angesichts der Vielzahl der Anforderungen und Nutzungskontexte eines elektronischen Dokuments nicht trivial. In dieser Arbeit werden aus der Hard-/Softwareverifikation bekannte Model-Checking-Verfahren mit Methoden zur Repräsentation von Ontologien kombiniert, um sowohl die Struktur des Dokuments als auch inhaltliche Zusammenhänge bei der Prüfung von Konsistenzkriterien berücksichtigen zu können. Als Spezifikationssprache für Konsistenzkriterien wird die neue temporale Beschreibungslogik ALCCTL vorgeschlagen. Grundlegende Eigenschaften wie Entscheidbarkeit, Ausdruckskraft und Komplexität werden untersucht. Die Adäquatheit und Praxistauglichkeit des Ansatzes werden in Fallstudien mit eLearning-Dokumenten evaluiert. Die Ergebnisse übertreffen bekannte Ansätze wie symbolisches Model-Checking oder Methoden zur Validierung von XML-Dokumenten in Performanz, Ausdruckskraft hinsichtlich der prüfbaren Kriterien und Flexibilität hinsichtlich des Dokumenttyps und -formats