Semantic Interoperability of Geospatial Ontologies: A Model-theoretic Analysis

People sometimes misunderstand each other, even when they use the same language to communicate. Often these misunderstandings happen when people use the same words to mean different things, in effect disagreeing about meanings. This thesis investigates such disagreements about meaning, considering them to be issues of semantic interoperability. This thesis explores semantic interoperability via a particular formal framework used to specify people’s conceptualizations of a given domain. This framework is called an ‘ontology,’ which is a collection of data and axioms written in a logical language equipped with a modeltheoretic semantics. The domain under consideration is the geospatial domain. Specifically, this thesis investigates to what extent two geospatial ontologies are semantically interoperable when they ‘agree’ on the meanings of certain basic terms and statements, but ‘disagree’ on others. This thesis defines five levels of semantic interoperability that can exist between two ontologies. Each of these levels is, in turn, defined in terms of six ‘compatibility conditions,’ which precisely describe how the results of queries to one ontology are compatible with the results of queries to another ontology. Using certain assumptions of finiteness, the semantics of each ontology is captured by a finite number of models, each of which is also finite. The set of all models of a given ontology is called its model class. The five levels of semantic interoperability are proven to correspond exactly to five particular relationships between the model classes of the ontologies. The exact level of semantic interoperability between ontologies can in some cases be computed; in other cases a heuristic can be used to narrow the possible levels of semantic interoperability. The main results are: (1) definitions of five levels of semantic interoperability based on six compatibility conditions; (2) proofs of the correspondence between levels of semantic interoperability and the model-class relation between two ontologies; and (3) a method for computing, given certain assumptions of finiteness, the exact level of semantic interoperability between two ontologies. These results define precisely, in terms of models and queries, the often poorly defined notion of semantic interoperability, thus providing a touchstone for clear definitions of semantic interoperability elsewhere

Visualization of state transition graphs

State transition graphs are important in computer science and engineering where they are used to analyze the behavior of computer-based systems. In such a graph nodes represent states a system can be in. Links, or directed edges, represent transitions between states. Research in visualization investigates the application of interactive computer graphics to understand large and complex data sets. Large state transition graphs fall into this category. They often contain tens of thousands of nodes, or more, and tens to hundreds of thousands of edges. Also, they describe system behavior at a low abstraction level. This hinders analysis and insight. This dissertation presents a number of techniques for the interactive visualization of state transition graphs. Much of the work takes advantage of multivariate data associated with nodes and edges. Using an experimental approach, several new methods were developed in close collaboration with a number of users. The following approaches were pursued: • Selection and projection. This technique provides the user with visual support to select a subset of node attributes. Consequently, the state transition graph is projected to 2D and visualized in a second, correlated visualization. • Attribute-based clustering. By specifying subsets of node attributes and clustering based on these, the user generates simplified abstractions of a state transition graph. Clustering generates hierarchical, relational, and metric data, which are represented in a single visualization. • User-defined diagrams. With this technique the user investigates state transition graphs with custom diagrams. Diagrams are parameterized by linking their graphical properties to the data. Diagrams are integrated in a number of correlated visualizations. • Multiple views on traces. System traces are linear paths in state transition graphs. This technique provides the user with different perspectives on traces. • Querying nodes and edges. Direct manipulation enables the user to interactively inspect and query state transition graphs. In this way relations and patterns can be investigated based on data associated with nodes and edges. This dissertation shows that interactive visualization can play a role during the analysis of state transition graphs. The ability to interrogate visual representations of such graphs allows users to enhance their knowledge of the modeled systems. It is shown how the above techniques enable users to answer questions about their data. A number of case studies, developed in collaboration with system analysts, are presented. Finally, solutions to challenges encountered during the development of the visualization techniques are discussed. Insights generic to the field of visualization are considered and directions for future work are recommended