Semantic Variability in the Interpretation of Geometries and Attributes in Geographic Information Systems

Abstract

Geographic Information Systems (GISs) allow analysts to manipulate geometric data in order to characterize spatial entities and compute qualitative and quantitative measures that describe their structure, distribution, and relationships. Analysts ensure that applying analytical operations is meaningful by interpreting the geometric data and the attributes that describe them. Currently, processes that require such interpretation are difficult to automate. In this dissertation, the problem is framed as one of ambiguous data: the geometry and attribute data stand as symbols for multiple distinct geometry concepts. The issue then lies in identifying how these geometric representations can be disambiguated and remodeled. Throughout this dissertation I contribute to this goal by 1) providing a typification of geometric and attribute data interpretations, 2) scrutinizing semantic and formal frameworks for interpretation models, and 3) empirically verifying the extent to which resulting theories reflect GIS practice. For the typification of geometry and attribute data I draw on existing insights in theories of GI science, formal ontologies and measurement theory, and also produce new theory. Firstly, the standard concepts of GI science insufficiently explain the semantics of the relation between quantity attributes and geometries. We therefore propose a novel formal theory of extensive measurement based on amount and quantity concepts and control and measure semantics, adapted to the context of GI science. Secondly, we needed a way to formally address the collection of all ways a particular entity could be interpreted. We provide a method for collecting interpretations of assumably the same entity in a single notion called a transcept, making use of point-of-view semantics and conceptual space theory. Thirdly, questions remained about how homeomerosity, a property of quantities which holds that a whole and its parts are of the same kind, can be defined in conceptual structures. We provide, as far as we know, the first definition of homeomerosity in a Formal Concept Analysis framework. Fourthly, the distinction between discrete and continuous geometries is crucial for geo-analysis, but is not well understood. We formally define multiple novel notions of discreteness and continuity that can be used to infer whether data structures suggest discrete or continuous representations using first-order logic and a basic set meta-theory. The problem of modeling geometry and attribute data interpretations is considered in the contexts of multiple formal and semantic frameworks. The first is one we defined based on higher-order logic with a semantics of domains of measurement, where some domain takes a role of a control domain and another the role of measure domain. Secondly, a framework of conceptual space partitioned through viewpoint semantics is considered, which allows representations of concepts as geometric entities. Thirdly, we apply the framework of Formal Concept Analysis (FCA), which is particularly suitable to model conceptual dualities, to define homeomerosity, and consider the duality between space and place. Finally, using the acquired insights, we interpret the formal semantics of logic in terms of extensional and intensional modes of reasoning to define discreteness and continuity.