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Bittner Thomas

On the Algebra of Rough Localization (Thesis Abstract)

Thomas Bittner
Department of Geoinformation
Technical University, Vienna
bittner@geoinfo.tuwien.ac.at

Motivation


Large effort is spent in "the full integration of geospatial data and geoprocessing resources into mainstream computing and the widespread use of interoperable, commercial geoprocessing software through the global information infrastructure" (OpenGIS 1998, p. iii). Geospatial data is "data which describes phenomena directly or indirectly with a location ... relative to the surface of Earth'' (OpenGIS 1998, p. 1). Interoperability is "the ability for a system or components of a system to provide information portability and interapplication, cooperative process control" (OpenGIS 1998, p. 74).

A clear understanding of the ontological and epistemological status of location is a basic precondition to achieve these goals. A clear understanding of the ontological status of location, i.e., what location is, is the basis for shareability of geospatial information. A clear understanding of the epistemological status of location, i.e., what do we know about the location of things, is the basis for representation of geospatial data.

In this thesis a unified view on ontological and epistemological aspects of location is provided. The ontological analysis results in the distinction between exact, vague, and rough localization. Based on this distinction a formal analysis of location is provided. The epistemological analysis shows that for geospatial objects only vague location can be known and represented.
The thesis proves the following hypothesis:
For geospatial objects only vague location can be measured, known, and represented.
Geoprocessing is based on operations on vague localization.


Rough Localization

Localization is a relation between spatial objects and regions of space (Casati and Varzi 1995).
This thesis distinguishes between exact localization, vague, and rough localization.
Exact localization is a relation between a spatial object and the unique region of space at which the object is located.
Vague localization is a relation between a spatial object and regions of space at which parts of the object are located.
Rough localization is vague localization between a spatial object and regions of space that form a regional partition.
From an ontological point of view rough localization is a special kind of vague localization. It is based on the existence of regional partitions.

The formal analysis concentrates on rough localization and assumes that the results also apply to vague localization in general. On the formal level this thesis discusses:
Formal models of exact and rough localization.
Relations between exact and rough localization.
Operations on exact and rough localization and their relations.
Aspects and assumptions of the representability of localizationon a computer.


Knowledge of Localization

The application of concepts of localization to spatial information systems has another aspect: It involves human knowledge of spatial objects and their localization in space. The questions: What do we know and what can we know about the localization of spatial objects, i.e., aspects of Epistemology, need to be considered.
In the context of geographic information systems we have to deal with phenomena of geographic kind. One important aspect of these phenomena is that we do not know their exact localization. This may have two reasons:
We do not know exactly what the spatial object is.
It is impossible to measure the exact localization of a spatial object.
Scientists in geographic information science refer to the first point as 'definitional uncertainty' and to the second point as 'locational uncertainty'.
For almost all phenomena in geographic space all we can ever know is vague localization. We do know that there exists one and only one region spatial objects are exactly located in each moment in time. In general we do not know the identity of this region. Often we can know, from observation, whether a region is a part of another region, overlaps another region, or does not overlap another region, i.e., we know its vague localization.

Rough Localization in GIS


Geographic information systems are supposed to model geographic reality based on their internal representation. Since these representations represent human knowledge they can represent only vague localization. GIS often ignore the fact that the exact localization of a spatial object is unknown, or not finitely representable, or both. The analysis in this thesis shows that numeric representations of semi-linear sets found in most vector GIS are incomplete representations of rough localization.
An important aspect of modeling is to perform operations. The analysis in this thesis shows, that operations on rough localization are different from operations on exact localization. In current vector GIS incomplete rough location is represented. Assume the representation is incomplete but consistent. On this representation of rough localization operations from the domain of exact location are performed resulting in another not necessarily consistent representation of rough localization.

The consequences of this analysis are:
GIS need to represent rough localization.
GIS operations need to be implemented as operations on rough localization

Bibliography


Casati, R. and A. Varzi (1995). "The Structure of Spatial Localization." Philosophical Studies 82(2): 205-239.
OpenGIS (1998). The OpenGIS Guide. Wayland, MA, Open GIS Consortium.

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