Epistemic Reasoning in OWL 2 DL

We extend the description logic SROIQ (OWL 2 DL) with the epistemic operator K and argue that unintended effects occur when imposing the semantics traditionally employed. Consequently, we identify the most expressive DL for which the traditional approach can still be adapted. For the epistemic extension of SROIQ and alike expressive DLs, we suggest a revised semantics that behaves more intuitively in these cases and coincides with the traditional semantics on less expressive DLs

Integrating ontologies and argumentation for decision-making in breast cancer

This thesis describes some of the problems in providing care for patients with breast cancer. These are then used to motivate the development of an extension to an existing theory of argumentation, which I call the Ontology-based Argumentation Formalism (OAF). The work is assessed in both theoretical and empirical ways. From a clinical perspective, there is a problem with the provision of care. Numerous reports have noted the failure to provide uniformly high quality care, as well as the number of deaths caused by medical care. The medical profession has responded in various ways, but one of these has been the development of Decision Support Systems (DSS). The evidence for the effectiveness of such systems is mixed, and the technical basis of such systems remains open to debate. However, one basis that has been used is argumentation. An important aspect of clinical practice is the use of the evidence from clinical trials, but these trials are based on the results in defined groups of patients. Thus when we use the results of clinical trials to reason about treatments, there are two forms of information we are interested in - the evidence from trials and the relationships between groups of patients and treatments. The relational information can be captured in an ontology about the groups of patients and treatments, and the information from the trials captured as a set of defeasible rules. OAF is an extension of an existing argumentation system, and provides the basis for an argumentation-based Knowledge Representation system which could serve as the basis for future DSS. In OAF, the ontology provides a repository of facts, both asserted and inferred on the basis of formulae in the ontology, as well as defining the language of the defeasible rules. The defeasible rules are used in a process of defeasible reasoning, where monotonic consistent chains of reasoning are used to draw plausible conclusions. This defeasible reasoning is used to generate arguments and counter-arguments. Conflict between arguments is defined in terms of inconsistent formulae in the ontology, and by using existing proposals for ontology languages we are able to make use of existing proposals and technologies for ontological reasoning. There are three substantial areas of novel work: I develop an extension to an existing argumentation formalism, and prove some simple properties of the formalism. I also provide a novel formalism of the practical syllogism and related hypothetical reasoning, and compare my approach to two other proposals in the literature. I conclude with a substantial case study based on a breast cancer guideline, and in order to do so I describe a methodology for comparing formal and informal arguments, and use the results of this to discuss the strengths and weaknesses of OAF. In order to develop the case study, I provide a prototype implementation. The prototype uses a novel incremental algorithm to construct arguments and I give soundness, completeness and time-complexity results. The final chapter of the thesis discusses some general lessons from the development of OAF and gives ideas for future work

Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure

In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and Magidor's ranked models and allows for the definition of defeasible inclusions. We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is in general $\Pi^P_2$-hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance checking under rational entailment and exploit it, with stratified negation, for computing the rational closure of simple KBs in polynomial time.Comment: Accepted for publication on Fundamenta Informatica

A Language for Inconsistency-Tolerant Ontology Mapping

Ontology alignment plays a key role in enabling interoperability among various data sources present in the web. The nature of the world is such, that the same concepts differ in meaning, often so slightly, which makes it difficult to relate these concepts. It is the omni-present heterogeneity that is at the core of the web. The research work presented in this dissertation, is driven by the goal of providing a robust ontology alignment language for the semantic web, as we show that description logics based alignment languages are not suitable for aligning ontologies. The adoption of the semantic web technologies has been consistently on the rise over the past decade, and it continues to show promise. The core component of the semantic web is the set of knowledge representation languages -- mainly the W3C (World Wide Web Consortium) standards Web Ontology Language (OWL), Resource Description Framework (RDF), and Rule Interchange Format (RIF). While these languages have been designed in order to be suitable for the openness and extensibility of the web, they lack certain features which we try to address in this dissertation. One such missing component is the lack of non-monotonic features, in the knowledge representation languages, that enable us to perform common sense reasoning. For example, OWL supports the open world assumption (OWA), which means that knowledge about everything is assumed to be possibly incomplete at any point of time. However, experience has shown that there are situations that require us to assume that certain parts of the knowledge base are complete. Employing the Closed World Assumption (CWA) helps us achieve this. Circumscription is a very well-known approach towards CWA, which provides closed world semantics by employing the idea of minimal models with respect to certain predicates which are closed. We provide the formal semantics of the notion of Grounded Circumscription, which is an extension of circumscription with desirable properties like decidability. We also provide a tableaux calculus to reason over knowledge bases under the notion of grounded circumscription. Another form of common sense logic, is default logic. Default logic provides a way to specify rules that, by default, hold in most cases but not necessarily in all cases. The classic example of such a rule is: If something is a bird then it flies. The power of defaults comes from the ability of the logic to handle exceptions to the default rules. For example, a bird will be assumed to fly by default unless it is an exception, i.e. it belongs to a class of birds that do not fly, like penguins. Interestingly, this property of defaults can be utilized to create mappings between concepts of different ontologies (knowledge bases). We provide a new semantics for the integration of defaults in description logics and show that it improves upon previously known results in literature. In this study, we give various examples to show the utility and advantages of using a default logic based ontology alignment language. We provide the semantics and decidability results of a default based mapping language for tractable fragments of description logics (or OWL). Furthermore, we provide a proof of concept system and qualitative analysis of the results obtained from the system when compared to that of traditional mapping repair techniques

Reasoning-Supported Quality Assurance for Knowledge Bases

The increasing application of ontology reuse and automated knowledge acquisition tools in ontology engineering brings about a shift of development efforts from knowledge modeling towards quality assurance. Despite the high practical importance, there has been a substantial lack of support for ensuring semantic accuracy and conciseness. In this thesis, we make a significant step forward in ontology engineering by developing a support for two such essential quality assurance activities

OWL and Rules

The relationship between the Web Ontology Language OWL and rule-based formalisms has been the subject of many discussions and research investigations, some of them controversial. From the many attempts to reconcile the two paradigms, we present some of the newest developments. More precisely, we show which kind of rules can be modeled in the current version of OWL, and we show how OWL can be extended to incorporate rules. We finally give references to a large body of work on rules and OWL

Combining open and closed world reasoning for the semantic web

Dissertação para obtenção do Grau de Doutor em InformáticaOne important problem in the ongoing standardization of knowledge representation languages for the Semantic Web is combining open world ontology languages, such as the OWL-based ones, and closed world rule-based languages. The main difficulty of such a combination is that both formalisms are quite orthogonal w.r.t. expressiveness and how decidability is achieved. Combining non-monotonic rules and ontologies is thus a challenging task that requires careful balancing between expressiveness of the knowledge representation language and the computational complexity of reasoning. In this thesis, we will argue in favor of a combination of ontologies and nonmonotonic rules that tightly integrates the two formalisms involved, that has a computational complexity that is as low as possible, and that allows us to query for information instead of calculating the whole model. As our starting point we choose the mature approach of hybrid MKNF knowledge bases, which is based on an adaptation of the Stable Model Semantics to knowledge bases consisting of ontology axioms and rules. We extend the two-valued framework of MKNF logics to a three-valued logics, and we propose a well-founded semantics for non-disjunctive hybrid MKNF knowledge bases. This new semantics promises to provide better efficiency of reasoning,and it is faithful w.r.t. the original two-valued MKNF semantics and compatible with both the OWL-based semantics and the traditional Well- Founded Semantics for logic programs. We provide an algorithm based on operators to compute the unique model, and we extend SLG resolution with tabling to a general framework that allows us to query a combination of non-monotonic rules and any given ontology language. Finally, we investigate concrete instances of that procedure w.r.t. three tractable ontology languages, namely the three description logics underlying the OWL 2 pro les.Fundação para a Ciência e Tecnologia - grant contract SFRH/BD/28745/200

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Inference as a data management problem

Inference over OWL ontologies with large A-Boxes has been researched as a data management problem in recent years. This work adopts the strategy of applying a tableaux-based reasoner for complete T-Box classification, and using a rule-based mechanism for scalable A-Box reasoning. Specifically, we establish for the classified T-Box an inference framework, which can be used to compute and materialise inference results. The inference we focus on is type inference in A-Box reasoning, which we define as the process of deriving for each A-Box instance its memberships of OWL classes and properties. As our approach materialises the inference results, it in general provides faster query processing than non-materialising techniques, at the expense of larger space requirement and slower update speed. When the A-Box size is suitable for an RDBMS, we compile the inference framework to triggers, which incrementally update the inference materialisation from both data inserts and data deletes, without needing to re-compute the whole inference. More importantly, triggers make inference available as atomic consequences of inserts or deletes, which preserves the ACID properties of transactions, and such inference is known as transactional reasoning. When the A-Box size is beyond the capability of an RDBMS, we then compile the inference framework to Spark programmes, which provide scalable inference materialisation in a Big Data system, and our evaluation considers up to reasoning 270 million A-Box facts. Evaluating our work, and comparing with two state-of-the-art reasoners, we empirically verify that our approach is able to perform scalable inference materialisation, and to provide faster query processing with comparable completeness of reasoning.Open Acces

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