On the Algebra of Rough Localization (Thesis Abstract)
Department of Geoinformation
Technical University, Vienna
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.
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.
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.
an ontological point of view rough localization is a special kind of
vague localization. It is based on the existence of regional partitions.
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
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.
in geographic information science refer to the first point as
'definitional uncertainty' and to the second point as 'locational
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
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.
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
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.