Description logics (DLs) are knowledge representation languages that provide the theoretical underpinning for modern ontology languages such as OWL and serve as the basis for the development of ontology reasoners and tools. Most modern ontology reasoners are based on optimized tableau algorithms, which perform reasoning by trying to build counter-models. More recently, another kind of reasoning algorithms has been introduced that, instead of building counter-models, directly derive logical consequences of axioms in the ontology using inference rules. Such consequence-based algorithms were first introduced for the EL family of DLs, and later extended to more expressive Horn DLs. However, up until now, consequence-based algorithms could not handle non-Horn features such as disjunctions. We consider several complementary aspects of consequence-based reasoning in this thesis. Firstly, we describe the parallelized consequence-based reasoner ELK, which is currently the fastest reasoner for EL ontologies. Secondly, we demonstrate how consequence-based algorithms can be extended to handle disjunctions using inference rules reminiscent of ordered resolution. Finally, we combine our consequence-based framework with methods based on tree decompositions, and thus obtain what we believe are the first fixed-parameter tractability results for subsumption reasoning in DLs.

A reutilização de conhecimento é uma tarefa chave para qualquer sistema computacional. Entretanto, o reúso indiscriminado desse conhecimento pode gerar resultados conflitantes com o objetivo de uso do conhecimento, levando sistemas a se comportarem de maneira imprevisível. Neste trabalho estudamos as consequências do reúso de conhecimento em ontologias baseadas em lógicas de descrição. Focamos principalmente nos problemas que podem ser causados pela fusão de ontologias. Investigamos e comparamos a capacidade das ferramentas de desenvolvimento de ontologias atuais de lidarem com esses problemas e como a teoria se desenvolveu para resolver os mesmos problemas. Realizamos a construção de um arcabouço lógico e de software, organizado na forma de um processo, que tem como objetivo auxiliar o projetista de ontologias a resolver conflitos advindos da fusão. O processo agrupa tarefas descritas normalmente na literatura em separado. Acreditamos que a união dessas abordagens leva a uma melhor solução de conflitos. Durante o desenvolvimento deste trabalho, concentramos nossos esforços principalmente no desenvolvimento de algoritmos para a construção de sub-ontologias maximais, onde os conflitos não ocorram, bem como a ordenação desses conjuntos segundo critérios comuns discutidos na literatura. Tais estratégias foram implementadas em software e testadas utilizando dados gerados automaticamente e dados reais. / Knowledge reuse is a key task during any system development. Nevertheless, careless knowledge reuse may generate conflicting outcomes regarding the system goal, leading such systems to unpredictable behaviour. With that in mind, during this research we studied the consequences of knowledge reuse in ontologies based on description logics. We focused mainly on conflicts arising from ontology merging. We investigated and compared the features developed for this purpose on ontology development tools and how the theory field proposed to deal with the same issues. We developed both a logical and a software framework grouped into a process that aims to help the ontology designer solve conflicts arising from ontology merging. The process groups common tasks that are normally described separately. We believe that the unification of these approaches should result in a better solution for the merging conflicts. We concentrated our efforts during this work on building algorithms for building maximal sub-ontologies where such conflicts are non-existent as well as means for ordering such sets according to a few relevance criteria commonly described at the literature. Such algorithms were implemented and tested against automatically generated and real data.

We consider the overlap between reasoning involved in <em>conjunctive query optimization</em> (CQO) and in tableaux-based approaches to reasoning about subsumption in <em>description logics</em> (DLs). In both cases, an underlying graph is created, searched and modified. This process is determined by a given <em>query</em> and <em>database schema</em> in the first case and by a given <em>description</em> and <em>terminology</em> in the second. The opportunities for overlap derive from an abundance of reductions of various schema languages to terminologies for common DL dialects, and from the fact that descriptions can in turn be viewed as queries that compute a single column. <br /><br /> Our main contributions are as follows. We present the design and implementation of a common graph utility that integrates the requirements for both CQO and DL reasoning. We then verify this model by also presenting the design and implementation for two drivers, one that implements a query optimizer for a conjunctive query language extended with descriptions, and one that implements a complete DL reasoner for a feature based DL dialect.

Indexing data for efficient search capabilities is a core problem in many domains of computer science. As applications centered around semantic data sources become more common, the need for more sophisticated indexing and querying capabilities arises. In particular, the need to search for specific information in the presence of a terminology or ontology (i.e. a set of logic based rules that describe concepts and their relations) becomes of particular importance, as the information a user seeks may exists as an entailment of the explicit data by means of the terminology. This variant on traditional indexing and search problems forms the foundation of a range of possible technologies for semantic data. In this work, we propose an ordering language for specifying partial orders over semantic data items modeled as descriptions in a description logic. We then show how these orderings can be used as the basis of a search tree index for processing \emph{concept searches} in the presence of a terminology. We study in detail the properties of the orderings and the associated index structure, and also explore a relationship between ordering descriptions called \emph{order refinement}. A sound and complete procedure for deciding refinement is given. We also empirically evaluate a prototype implementation of our index structure, validating its potential efficacy in semantic query problems.

We consider the overlap between reasoning involved in <em>conjunctive query optimization</em> (CQO) and in tableaux-based approaches to reasoning about subsumption in <em>description logics</em> (DLs). In both cases, an underlying graph is created, searched and modified. This process is determined by a given <em>query</em> and <em>database schema</em> in the first case and by a given <em>description</em> and <em>terminology</em> in the second. The opportunities for overlap derive from an abundance of reductions of various schema languages to terminologies for common DL dialects, and from the fact that descriptions can in turn be viewed as queries that compute a single column. <br /><br /> Our main contributions are as follows. We present the design and implementation of a common graph utility that integrates the requirements for both CQO and DL reasoning. We then verify this model by also presenting the design and implementation for two drivers, one that implements a query optimizer for a conjunctive query language extended with descriptions, and one that implements a complete DL reasoner for a feature based DL dialect.

Indexing data for efficient search capabilities is a core problem in many domains of computer science. As applications centered around semantic data sources become more common, the need for more sophisticated indexing and querying capabilities arises. In particular, the need to search for specific information in the presence of a terminology or ontology (i.e. a set of logic based rules that describe concepts and their relations) becomes of particular importance, as the information a user seeks may exists as an entailment of the explicit data by means of the terminology. This variant on traditional indexing and search problems forms the foundation of a range of possible technologies for semantic data. In this work, we propose an ordering language for specifying partial orders over semantic data items modeled as descriptions in a description logic. We then show how these orderings can be used as the basis of a search tree index for processing \emph{concept searches} in the presence of a terminology. We study in detail the properties of the orderings and the associated index structure, and also explore a relationship between ordering descriptions called \emph{order refinement}. A sound and complete procedure for deciding refinement is given. We also empirically evaluate a prototype implementation of our index structure, validating its potential efficacy in semantic query problems.

The Web Ontology Language OWL is based on the highly expressive description logic SROIQ, which allows OWL ontology users to employ out-of-the-box reasoners to compute information that is not only explicitly asserted, but entailed by the ontology. Explanation facilities for entailments of OWL ontologies form an essential part of ontology development tools, as they support users in detecting and repairing errors in potentially large and highly complex ontologies, thus helping to ensure ontology quality. Justifications, minimal subsets of an ontology that are sufficient for an entailment to hold, are currently the prevalent form of explanation in OWL ontology development tools. They have been found to significantly reduce the time and effort required to debug erroneous entailments. A large number of entailments, however, have not only one but many justifications, which can make it considerably more challenging for a user to find a suitable repair for the entailment.In this thesis, we investigate the relationships between multiple justifications for both single and multiple entailments, with the goal of exploiting this justificatory structure in order to devise new coping strategies for multiple justifications. We describe various aspects of the justificatory structure of OWL ontologies, such as shared axiom cores and structural similarities. We introduce a model for measuring user effort in the debugging process and propose debugging strategies that exploit the justificatory structure in order to reduce user effort. Finally, an analysis of a large corpus of ontologies from the biomedical domain reveals that OWL ontologies used in practice frequently exhibit a rich justificatory structure.

Description logics are a family of logics that provide formalisms for representing and reasoning about knowledge, based on describing concepts, in a structured and formally well-understood way. They provide the logical foundation for the web ontology language (OWL), which increased awareness of them recently. The most popular techniques for decision procedures for description logics are tableau reasoning methods, which have a long tradition and are well established in automated reasoning. This thesis investigates the possibility of finding a general and optimised blocking mechanism for description logics with the finite model property. It suggests that, while the high branching factor for unrestricted blocking reduces its performance, suitable control of the application of the blocking rule can make the performance acceptable while preserving termination. This claim is supported by experiments that compare the performance of two sample controlled versions of unrestricted blocking. In order to show the generality and power of controlled versions of unrestricted blocking, it is shown how some of the mainstream and most successful standard blocking mechanisms can be approximated as restricted forms of unrestricted blocking. These approximations have the advantage of always being sound compared to their standard versions, which are known to be sound only for some logics. Here, a variation of unrestricted blocking which can ensure strong termination is also introduced. This is done through introducing a new rule that uses the inequality expressions introduced by the blocking rule. The weak termination property of unrestricted blocking is one of its weak points which by this variant of blocking can be addressed. The work presented in this thesis should be of value to people who are working on generalising different aspects of reasoning methods. As blocking plays a critical role in termination of tableau provers, exploration of different variations of unrestricted blocking introduced here may be also of interest for the artificial intelligence researcher.

A reutilização de conhecimento é uma tarefa chave para qualquer sistema computacional. Entretanto, o reúso indiscriminado desse conhecimento pode gerar resultados conflitantes com o objetivo de uso do conhecimento, levando sistemas a se comportarem de maneira imprevisível. Neste trabalho estudamos as consequências do reúso de conhecimento em ontologias baseadas em lógicas de descrição. Focamos principalmente nos problemas que podem ser causados pela fusão de ontologias. Investigamos e comparamos a capacidade das ferramentas de desenvolvimento de ontologias atuais de lidarem com esses problemas e como a teoria se desenvolveu para resolver os mesmos problemas. Realizamos a construção de um arcabouço lógico e de software, organizado na forma de um processo, que tem como objetivo auxiliar o projetista de ontologias a resolver conflitos advindos da fusão. O processo agrupa tarefas descritas normalmente na literatura em separado. Acreditamos que a união dessas abordagens leva a uma melhor solução de conflitos. Durante o desenvolvimento deste trabalho, concentramos nossos esforços principalmente no desenvolvimento de algoritmos para a construção de sub-ontologias maximais, onde os conflitos não ocorram, bem como a ordenação desses conjuntos segundo critérios comuns discutidos na literatura. Tais estratégias foram implementadas em software e testadas utilizando dados gerados automaticamente e dados reais. / Knowledge reuse is a key task during any system development. Nevertheless, careless knowledge reuse may generate conflicting outcomes regarding the system goal, leading such systems to unpredictable behaviour. With that in mind, during this research we studied the consequences of knowledge reuse in ontologies based on description logics. We focused mainly on conflicts arising from ontology merging. We investigated and compared the features developed for this purpose on ontology development tools and how the theory field proposed to deal with the same issues. We developed both a logical and a software framework grouped into a process that aims to help the ontology designer solve conflicts arising from ontology merging. The process groups common tasks that are normally described separately. We believe that the unification of these approaches should result in a better solution for the merging conflicts. We concentrated our efforts during this work on building algorithms for building maximal sub-ontologies where such conflicts are non-existent as well as means for ordering such sets according to a few relevance criteria commonly described at the literature. Such algorithms were implemented and tested against automatically generated and real data.

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