15 research outputs found

    Reasoning with Forest Logic Programs and f-hybrid Knowledge Bases

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    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

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    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

    And-or tableaux for fixpoint logics with converse: LTL, CTL, PDL and CPDL

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    Over the last forty years, computer scientists have invented or borrowed numerous logics for reasoning about digital systems. Here, I would like to concentrate on three of them: Linear Time Temporal Logic (LTL), branching time Computation Tree temporal Logic (CTL), and Propositional Dynamic Logic (PDL), with and without converse. More specifically, I would like to present results and techniques on how to solve the satisfiability problem in these logics, with global assumptions, using the tableau method. The issues that arise are the typical tensions between computational complexity, practicality and scalability. This is joint work with Linh Anh Nguyen, Pietro Abate, Linda Postniece, Florian Widmann and Jimmy Thomson

    Action, Time and Space in Description Logics

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    Description Logics (DLs) are a family of logic-based knowledge representation (KR) formalisms designed to represent and reason about static conceptual knowledge in a semantically well-understood way. On the other hand, standard action formalisms are KR formalisms based on classical logic designed to model and reason about dynamic systems. The largest part of the present work is dedicated to integrating DLs with action formalisms, with the main goal of obtaining decidable action formalisms with an expressiveness significantly beyond propositional. To this end, we offer DL-tailored solutions to the frame and ramification problem. One of the main technical results is that standard reasoning problems about actions (executability and projection), as well as the plan existence problem are decidable if one restricts the logic for describing action pre- and post-conditions and the state of the world to decidable Description Logics. A smaller part of the work is related to decidable extensions of Description Logics with concrete datatypes, most importantly with those allowing to refer to the notions of space and time

    Pseudo-contractions as Gentle Repairs

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    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

    Incremental decision procedures for modal logics with nominals and eventualities

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    This thesis contributes to the study of incremental decision procedures for modal logics with nominals and eventualities. Eventualities are constructs that allow to reason about the reflexive-transitive closure of relations. Eventualities are an essential feature of temporal logics and propositional dynamic logic (PDL). Nominals extend modal logics with the possibility to reason about state equality. Modal logics with nominals are often called hybrid logics. Incremental procedures are procedures that can potentially solve a problem by performing only the reasoning steps needed for the problem in the underlying calculus. We begin by introducing a class of syntactic models called demos and showing how demos can be used for obtaining nonincremental but worst-case optimal decision procedures for extensions of PDL with nominals, converse and difference modalities. We show that in the absence of nominals, such nonincremental procedures can be refined into incremental demo search procedures, obtaining a worst-case optimal decision procedure for modal logic with eventualities. We then develop the first incremental decision procedure for basic hybrid logic with eventualities, which we eventually extend to deal with hybrid PDL. The approach in the thesis suggests a new principled design of modular, incremental decision procedures for expressive modal logics. In particular, it yields the first incremental procedures for modal logics containing both nominals and eventualities.Diese Dissertation untersucht inkrementelle Entscheidungsverfahren für Modallogiken mit Nominalen und Eventualities. Eventualities sind Konstrukte, die erlauben, über den reflexiv-transitiven Abschluss von Relationen zu sprechen. Sie sind ein Schlüsselmerkmal von Temporallogiken und dynamischer Aussagenlogik (PDL). Nominale erweitern Modallogik um die Möglichkeit, über Gleichheit von Zuständen zu sprechen. Modallogik mit Nominalen nennt man Hybridlogik. Inkrementell ist ein Verfahren dann, wenn es ein Problem so lösen kann, dass für die Lösung nur solche Schritte in dem zugrundeliegenden Kalkül gemacht werden, die für das Problem relevant sind. Wir führen zunächst eine Klasse syntaktischer Modelle ein, die wir Demos nennen. Wir nutzen Demos um nichtinkrementelle aber laufzeitoptimale Entscheidungsverfahren für Erweiterungen von PDL zu konstruieren. Wir zeigen, dass im Fall ohne Nominale solche Verfahren durch algorithmische Verfeinerung zu inkrementellen Verfahren ausgebaut werden können. Insbesondere erhalten wir so ein optimales Verfahren für Modallogik mit Eventualities. Anschließend entwickeln wir das erste inkrementelle Verfahren für Hybridlogik mit Eventualities, welches wir schließlich auf hybrides PDL erweitern. Die Dissertation vermittelt einen neuen Ansatz zur Konstruktion modularer, inkrementeller Entscheidungsverfahren für expressive Modallogiken. Insbesondere liefert der Ansatz die ersten inkrementellen Verfahren für Modallogiken mit Nominalen und Eventualities

    Derivation methods for hybrid knowledge bases with rules and ontologies

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    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

    Reasoning in description logics using resolution and deductive databases

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    Approximate Assertional Reasoning Over Expressive Ontologies

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    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
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