Extending Descriptions Logics (DLs) with a temporal dimension to aid in the ability to model meaningful temporal information is an active and popular research area that has gathered a lot of attention over recent years. DLs underpin the Web Ontology Language (OWL) which offers a way to describe ontologies for the semantic web. Representing temporal information in ontologies plays an important role, specifically for those ontologies where time information is inherently embedded in the information they describe. This is very common for ontologies in the bio-health domain, for example ontologies that describe the development of anatomies of biological entities, stage based development, evolution of diseases and so on. As expressive as DLs are, given that they are fragments of First Order Logic, they are static in nature and are limited in what they can express from a temporal view point, hence the surge in temporal extensions to DLs over recent years. In this thesis we investigate the use of temporal extensions of DLs as suitable representations for the temporal information required for bio-health ontologies. We first set out to find out exactly what types of temporal information need to be modelled, before going on to evaluate current temporal extensions and representations to determine their suitability. We then go on to introduce several new temporal extensions to DLs and evaluate their suitability.

Most of the research on temporalized Description Logics (DLs) has concentrated on the case where temporal operators can occur within DL concept descriptions. In this setting, reasoning usually becomes quite hard if rigid roles, i.e., roles whose interpretation does not change over time, are available. In this paper, we consider the case where temporal operators are allowed to occur only in front of DL axioms (i.e., ABox assertions and general concept inclusion axioms), but not inside of concepts descriptions. As the temporal component, we use linear temporal logic (LTL) and in the DL component we consider the basic DL ALC. We show that reasoning in the presence of rigid roles becomes considerably simpler in this setting.

Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics - which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equational theories. In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics. / This report has also appeared as Report No. 03-03, Department of Computer Science, The University of Iowa.

Fuzzy Description Logics (FDLs) combine classical Description Logics with the semantics of Fuzzy Logics in order to represent and reason with vague knowledge. Most FDLs using truth values from the interval [0; 1] have been shown to be undecidable in the presence of a negation constructor and general concept inclusions. One exception are those FDLs whose semantics is based on the infinitely valued Gödel t-norm (G). We extend previous decidability results for the FDL G-ALC to deal with complex role inclusions, nominals, inverse roles, and qualified number restrictions. Our novel approach is based on a combination of the known crispification technique for finitely valued FDLs and an automata-based procedure for reasoning in G-ALC.

The verification problem for action logic programs with non-terminating behaviour is in general undecidable. In this paper, we consider a restricted setting in which the problem becomes decidable. On the one hand, we abstract from the actual execution sequences of a non-terminating program by considering infinite sequences of actions defined by a Büchi automaton. On the other hand, we assume that the logic underlying our action formalism is a decidable description logic rather than full first-order predicate logic.

Le domaine de la logistique implique souvent la résolution de problèmes combinatoires complexes. Ces derniers font également implicitement référence à des processus, acteurs, activités et méthodes concernant divers aspects qu'il faut considérer. Ainsi, un même problème peut faire intervenir des processus de vente/achat, transport/livraison et gestion de stock. Ces processus sont tellement divers et interconnectés qu'il est difficile pour un logisticien de tous les maîtriser. Dans cette thèse, nous proposons l'explicitation, par le biais d'ontologies, de connaissances conceptuelles et sémantiques concernant les processus logistiques. Ces connaissances explicites sont alors mises à contribution pour construire un système à base de connaissances permettant de guider les logisticiens dans la construction, de façon incrémentale et semi-automatique, de solutions informatiques à un problème qui leur est posé à un moment donné. Nous mettons en oeuvre une ontologie concernant le domaine de la logistique connectée à une ontologie associée à la problématique de l'optimisation. Nous établissons ainsi un lien sémantique explicite entre le domaine de la logistique et celui de l'optimisation. Cela permet aux logisticiens d'identifier de façon précise et sans ambigüité le problème logistique auquel il est confronté et les problèmes d'optimisation associés. L'identification des problèmes conduit alors à un processus de choix des solutions allant du choix du processus logistique précis à mettre en oeuvre à celui de la méthode de résolution du problème combinatoire et cela jusqu'à la découverte du composant informatique à invoquer et qui est matérialisé par un service web. L'approche que nous avons adoptée et mise en oeuvre a été expérimentée avec les problèmes de routage de véhicules, le problème de transport ferroviaire de passagers et le problème de terminaux de conteneurs. / Logistics problems are often complex combinatorial problems. These may also implicitly refer to the processes, actors, activities, and methods concerning various aspects that need to be considered. Thus the same process may involve the processes of sale/purchase, transport/delivery, and stock management. These processes are so diverse and interconnected that it is difficult for a logistic expert to compete all of them. In this thesis, we propose the explications with the help of ontologies of conceptual ans semantic knowledge concerning the logistic processes. This explicit knowledge is then used to develop a reasoning system to guide the logistic expert for an incremental and semi-automatic construction of a software solution to an instantly posed problem. We define an ontology concerning the inter-connected logistics and associated optimization problem. We, henceforth, establish an explicit semantic link between the domains of logistics and the optimization. It may allow the logistic expert to identify precisely and unambiguously the confronted logistic problem and the associated optimization problem. The identification of the problems then leads to a process to choose the solutions ranging from the choice of the precise logistic process to be implemented to that of the method to solve the combinatorial problem until the discovery of the software component to be invoked and which is implemented by a web service. The approach we have adopted and implemented has been experimented with the "Vehicle Routing Problems", the "Passenger Train Problem" and the "Container Terminal problems".