Count Distinct Semantic Queries over Multiple Linked Datasets

In this paper, we revise count distinct queries and their semantics over datasets with incomplete knowledge, which is a typical case for the linked data integration scenario where datasets are viewed as ontologies. We focus on counting individuals present in the signature of the ontology. Specifically, we investigate the Certain Epistemic Count (CEC) and the Possible Epistemic Count (PEC) interval based semantics. In the case of CEC semantics, we propose an algorithm for its evaluation and we prove its correctness under a practical constraint of the queried ontology. We conduct and report experiments with the implementation of the proposed algorithm. We also prove decidability of the PEC semantics

A Logical Geo-Ontology Design Pattern for Quantifying over Types

Ontology design patterns ease the engineering of ontologies, improve their quality, foster reusability, and support the alignment of ontologies by acting as common building blocks or strategies for reoccurring modeling problems. This makes ontology design patterns key enablers of semantic interoperability and, hence, a crucial technology for representing the body of knowledge of such heterogeneous domains as the geosciences. While different types of patterns can be distinguished, existing work on geo-ontology design patterns has solely focused on content patterns, i.e., design solutions for domain classes and relationships. In this work, we propose a logical pattern that addresses a frequent modeling problem that has hampered the development of sophisticated geo-ontologies in the past, namely how to model the quantification over types. We argue for the need for such a pattern, explain why it is difficult to model, demonstrate how to implement it using the Web Ontology Language OWL, and finally show how it can be applied to modeling concepts such as biodiversity

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