Concrete domains have been introduced in Description Logic (DL) to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. The primary research goal in this context was to find restrictions on the concrete domain such that its integration into certain DLs preserves decidability or tractability. In this paper, we investigate the abstract expressive power of logics extended with concrete domains, namely which classes of first-order interpretations can be expressed using these logics. In the first part of the paper, we show that, under natural conditions on the concrete domain D (which also play a role for decidability), extensions of first-order logic (FOL) or 𝒜ℒ𝒞 with D share important formal properties with FOL, such as the compactness and the Löwenheim-Skolem property. Nevertheless, their abstract expressive power need not be contained in that of FOL. In the second part of the paper, we investigate whether finitely bounded homogeneous structures, which preserve decidability if employed as concrete domains, can be used to express certain universal first-order sentences, which then could be added to DL knowledge bases without destroying decidability. We show that this requires rather strong conditions on said sentences or an extended scheme for integrating the concrete domain that leads to undecidability.

Building and mantaining large-scale ontologies is an error-prone task. It is thus not uncommon to find unwanted or unexpected consequences that follow implicitely from the restrictions in the ontology. To understand and correct these consequences, it is helpful to find the specific portions of the ontology that are responsible for them. Axiom-pinpointing is the task of finding minimal subontologies that entail a given consequence, also called MinAs. In this work we look at the task of computing all the MinAs by means of modified decision procedures. We first show that tableaux- and automata-based decision procedures can be transformed into pinpointing algorithms that output a (compact) representation of the set of all MinAs. We then explore the complexity of the problem.

Many information sources can be viewed as collections of objects and descriptions about objects. The relationship between objects is often characterized by a set of constraints that semantically encode background knowledge of some domain. The most straightforward and fundamental way to access information in these repositories is to search for objects that satisfy certain selection criteria. This work considers a description logics (DL) based representation of such information sources and object queries, which allows for automated reasoning over the constraints accompanying objects. Formally, a knowledge base K=(T, A) captures constraints in the terminology (a TBox) T, and objects with their descriptions in the assertions (an ABox) A, using some DL dialect L. In such a setting, object descriptions are L-concepts and object identifiers correspond to individual names occurring in K. Correspondingly, object queries are the well known problem of instance retrieval in the underlying DL knowledge base K, which returns the identifiers of qualifying objects. This work generalizes instance retrieval over knowledge bases to provide users with answers in which both identifiers and descriptions of qualifying objects are given. The proposed query paradigm, called assertion retrieval, is favoured over instance retrieval since it provides more informative answers to users. A more compelling reason is related to performance: assertion retrieval enables a transfer of basic relational database techniques, such as caching and query rewriting, in the context of an assertion retrieval algebra. The main contributions of this work are two-fold: one concerns optimizing the fundamental reasoning task that underlies assertion retrieval, namely, instance checking, and the other establishes a query compilation framework based on the assertion retrieval algebra. The former is necessary because an assertion retrieval query can entail a large volume of instance checking requests in the form of K|= a:C, where "a" is an individual name and "C" is a L-concept. This work thus proposes a novel absorption technique, ABox absorption, to improve instance checking. ABox absorption handles knowledge bases that have an expressive underlying dialect L, for instance, that requires disjunctive knowledge. It works particularly well when knowledge bases contain a large number of concrete domain concepts for object descriptions. This work further presents a query compilation framework based on the assertion retrieval algebra to make assertion retrieval more practical. In the framework, a suite of rewriting rules is provided to generate a variety of query plans, with a focus on plans that avoid reasoning w.r.t. the background knowledge bases when sufficient cached results of earlier requests exist. ABox absorption and the query compilation framework have been implemented in a prototypical system, dubbed CARE Assertion Retrieval Engine (CARE). CARE also defines a simple yet effective cost model to search for the best plan generated by query rewriting. Empirical studies of CARE have shown that the proposed techniques in this work make assertion retrieval a practical application over a variety of domains.

Many information sources can be viewed as collections of objects and descriptions about objects. The relationship between objects is often characterized by a set of constraints that semantically encode background knowledge of some domain. The most straightforward and fundamental way to access information in these repositories is to search for objects that satisfy certain selection criteria. This work considers a description logics (DL) based representation of such information sources and object queries, which allows for automated reasoning over the constraints accompanying objects. Formally, a knowledge base K=(T, A) captures constraints in the terminology (a TBox) T, and objects with their descriptions in the assertions (an ABox) A, using some DL dialect L. In such a setting, object descriptions are L-concepts and object identifiers correspond to individual names occurring in K. Correspondingly, object queries are the well known problem of instance retrieval in the underlying DL knowledge base K, which returns the identifiers of qualifying objects. This work generalizes instance retrieval over knowledge bases to provide users with answers in which both identifiers and descriptions of qualifying objects are given. The proposed query paradigm, called assertion retrieval, is favoured over instance retrieval since it provides more informative answers to users. A more compelling reason is related to performance: assertion retrieval enables a transfer of basic relational database techniques, such as caching and query rewriting, in the context of an assertion retrieval algebra. The main contributions of this work are two-fold: one concerns optimizing the fundamental reasoning task that underlies assertion retrieval, namely, instance checking, and the other establishes a query compilation framework based on the assertion retrieval algebra. The former is necessary because an assertion retrieval query can entail a large volume of instance checking requests in the form of K|= a:C, where "a" is an individual name and "C" is a L-concept. This work thus proposes a novel absorption technique, ABox absorption, to improve instance checking. ABox absorption handles knowledge bases that have an expressive underlying dialect L, for instance, that requires disjunctive knowledge. It works particularly well when knowledge bases contain a large number of concrete domain concepts for object descriptions. This work further presents a query compilation framework based on the assertion retrieval algebra to make assertion retrieval more practical. In the framework, a suite of rewriting rules is provided to generate a variety of query plans, with a focus on plans that avoid reasoning w.r.t. the background knowledge bases when sufficient cached results of earlier requests exist. ABox absorption and the query compilation framework have been implemented in a prototypical system, dubbed CARE Assertion Retrieval Engine (CARE). CARE also defines a simple yet effective cost model to search for the best plan generated by query rewriting. Empirical studies of CARE have shown that the proposed techniques in this work make assertion retrieval a practical application over a variety of domains.

Thèse (M.Inf.) -- Université du Québec à Chicoutimi, programme extensionné de l'Université du Québec à Montréal, 2004. / Bibliogr.: f. [109]-117. Document électronique également accessible en format PDF. CaQCU

[pt] Este trabalho aborda problemas de projeto de ontologias tratando-as como teorias e definindo um conjunto de operações que mapeiam ontologias em ontologias, incluindo suas restrições. Inicialmente, o trabalho resume o conhecimento básico necessário para definir a classe de ontologias utilizada e propõe quatro operações para manipular ontologias. Em seguida, mostra o funcionamento destas operações e como elas podem ajudar na criação de novas ontologias. O cerne do trabalho mostra a implementação destas operações em um plug-in do Protégé, detalhando sua arquitetura e incluindo casos de uso. / [en] This work addresses ontology design problems by treating ontologies as theories and by defining a set of operations that map ontologies into ontologies, including their constraints. The work first summarizes the base knowledge needed to define the class of ontologies used and proposes four operations to manipulate them. It then shows how the operations work and how they may help design new ontologies. The core of this work is describing the implementation of the operations over a Protégé plug-in, detailing the architecture and including case-use examples.

[pt] Integração de dados refere-se ao problema de combinar dados que estão armazenados em diferentes fontes, fornecendo ao usuário uma visão unificada dos dados. As consultas são então expressas em um esquema global ou esquema mediado, que deve incluir restrições de integridade que contribuam para um entendimento correto sobre o que a semântica das fontes de dados do ambiente de mediação tem em comum. Esta tese endereça o problema de modelar as restrições de um esquema mediado a partir das restrições dos esquemas importados e dos mapeamentos de esquemas. Argumenta-se que as restrições devem ser modeladas como o ínfimo das restrições dos esquemas exportados, depois de traduzidos para um vocabulário comum. Desta forma, assegura-se que os usuários do esquema mediado interpretarão os resultados das consultas corretamente. Para uma família expressiva de restrições, esta tese mostra como computar eficientemente o ínfimo de conjuntos de restrições. / [en] Data integration refers to the problem of combining data stored in different sources, providing users with a unified view of the data. Queries are then expressed in terms of a global or mediated schema, which should include integrity constraints that contribute to a correct understanding of what the semantics of the data sources have in common. This thesis addresses the problem of modeling the constraints of a mediated schema from the imported schemas constraints and mappings. It argues that the constraints should be modeled as the greatest lower bound of the constraints of the export schemas, after appropriate translation to a common vocabulary. This assures that users of the mediated schema will correctly interpret query results. For a rich family of constraints, it shows how to efficiently compute the greatest lower bound of sets of constraints.

Ontological database management systems are a powerful tool that combine traditional database techniques with ontological reasoning methods. In this setting, a classical extensional database is enriched with an ontology, or a set of logical assertions, that describe how new, intensional knowledge can be derived from the extensional data. Conjunctive queries are therefore answered against this combined knowledge base of extensional and intensional data. Many languages that represent ontologies have been introduced in the literature. In this thesis we will focus on existential rules (also called tuple-generating dependencies or Datalog^± rules), and three established languages in this area, namely guarded-based rules, sticky rules and weakly-acyclic rules. The main goal of the thesis is to enrich these languages with non-deterministic constructs (i.e. disjunctions) and investigate the complexity of the answering conjunctive queries under these extended languages. As is common in the literature, we will distinguish between combined complexity, where the database, the ontology and the query are considered as input, and data complexity, where only the database is considered as input. The latter case is relevant in practice, as usually the ontology and the query can be considered as fixed, and are usually much smaller than the database itself. After giving appropriate definitions to extend the considered languages to disjunctive existential rules, we establish a series of complexity results, completing the complexity picture for each of the above languages, and four different query languages: arbitrary conjunctive queries, bounded (hyper-)treewidth queries, acyclic queries and atomic queries. For the guarded-based languages, we show a strong 2EXPTIME lower bound for general queries that holds even for fixed ontologies, and establishes 2EXPTIME-completeness of the query answering problem in this case. For acyclic queries, the complexity can be reduced to EXPTIME, if the predicate arity is bounded, and the problem even becomes tractable for certain restricted languages, if only atomic queries are used. For ontologies represented by sticky disjunctive rules, we show that the problem becomes undecidable, even in the case of data complexity and atomic queries. Finally, for weakly-acyclic rules, we show that the complexity increases from 2EXPTIME to coN2EXPTIME in general, and from tractable to coNP in case of the data complexity, independent of which query language is used. After answering the open complexity questions, we investigate applications and relevant consequences of our results for description logics and give two generic complexity statements, respectively, for acyclic and general conjunctive query answering over description logic knowledge bases. These generic results allow for an easy determination of the complexity of this reasoning task, based on the expressivity of the considered description logic.

The World Wide Web contains large amounts of data, and in most cases this data has no explicit structure. The lack of structure makes it difficult for automated agents to understand and use such data. A step towards a more structured World Wide Web is the Semantic Web, which aims at introducing semantics to data on the World Wide Web. One of the key technologies in this endeavour are ontologies, which provide a means for modeling a domain of interest and are used for search and integration of data. In recent years many ontologies have been developed. To be able to use multiple ontologies it is necessary to align them, i.e., find inter-ontology relationships. However, developing and aligning ontologies is not an easy task and it is often the case that ontologies and their alignments are incorrect and incomplete. This can be a problem for semantically-enabled applications. Incorrect and incomplete ontologies and alignments directly influence the quality of the results of such applications, as wrong results can be returned and correct results can be missed. This thesis focuses on the problem of completing ontologies and ontology networks. The contributions of the thesis are threefold. First, we address the issue of completing the is-a structure and alignment in ontologies and ontology networks. We have formalized the problem of completing the is-a structure in ontologies as an abductive reasoning problem and developed algorithms as well as systems for dealing with the problem. With respect to the completion of alignments, we have studied system performance in the Ontology Alignment Evaluation Initiative, a yearly evaluation campaign for ontology alignment systems. We have also addressed the scalability of ontology matching, which is one of the current challenges, by developing an approach for reducing the search space when generating the alignment.Second, high quality completion requires user involvement. As users' time and effort are a limited resource we address the issue of limiting and facilitating user interaction in the completion process. We have conducted a broad study of state-of-the-art ontology alignment systems and identified different issues related to the process. We have also conducted experiments to assess the impact of user errors in the completion process. While the completion of ontologies and ontology networks can be done at any point in the life-cycle of ontologies and ontology networks, some of the issues can be addressed already in the development phase. The third contribution of the thesis addresses this by introducing ontology completion and ontology alignment into an existing ontology development methodology.

Description logics (DLs) are used to represent knowledge of an application domain and provide standard reasoning services to infer consequences of this knowledge. However, classical DLs are not suited to represent vagueness in the description of the knowledge. We consider a combination of DLs and Fuzzy Logics to address this task. In particular, we consider the t-norm-based semantics for fuzzy DLs introduced by Hájek in 2005. Since then, many tableau algorithms have been developed for reasoning in fuzzy DLs. Another popular approach is to reduce fuzzy ontologies to classical ones and use existing highly optimized classical reasoners to deal with them. However, a systematic study of the computational complexity of the different reasoning problems is so far missing from the literature on fuzzy DLs. Recently, some of the developed tableau algorithms have been shown to be incorrect in the presence of general concept inclusion axioms (GCIs). In some fuzzy DLs, reasoning with GCIs has even turned out to be undecidable. This work provides a rigorous analysis of the boundary between decidable and undecidable reasoning problems in t-norm-based fuzzy DLs, in particular for GCIs. Existing undecidability proofs are extended to cover large classes of fuzzy DLs, and decidability is shown for most of the remaining logics considered here. Additionally, the computational complexity of reasoning in fuzzy DLs with semantics based on finite lattices is analyzed. For most decidability results, tight complexity bounds can be derived.