Imprecision in spatial data arises from the granularity or resolution at which observations of phenomena are made, and from the limitations imposed by computational representations, processing and presentational media. Precision is an important component of spatial data quality, and a key to appropriate integration of collections of data sets. Previous work of the author provides a theoretical foundation for imprecision of spatial data resulting from finite granularities, and gives the beginnings of an approach to reasoning with such data using methods similar to rough set theory. This paper develops the theory further, and extends the work to a model that includes both spatial and semantic components. Notions such as observation, schema, frame of discernment and vagueness are examined and formalised. Keywords: GIS, imprecision, vagueness, resolution, spatial reasoning, data quality, uncertainty. Computers, Environment and Urban Systems 2 1. INTRODUCTION We now live in a world of ...

. Previous recent research on human wayfinding has focused primarily on mental representations rather than processes of wayfinding. This paper presents a formal model of some aspects of the process of wayfinding, where appropriate elements of human perception and cognition are formally realized using image schemata and affordances. The goal-driven reasoning chain that leads to action begins with incomplete and imprecise knowledge derived from imperfect observations of space. Actions result in further observations, derived knowledge and, recursively, further actions, until the goal is achieved or the wayfinder gives up. This paper gives a formalization of this process, using a modal extension to classical propositional logic to represent incomplete knowledge. Both knowledge and action are represented through a wayfinding graph. A special case of wayfinding in a building, that is finding one's way through an airport, is used to demonstrate the formal model. Keywords. Wayfind...

Precision is a key component of spatial data quality and in this era of globally distributed spatial data it is essential to be able to integrate multiple distributed data sets with heterogeneous levels of precision. Imprecision arises through limitations on semantic and geometric resolution of data representations. Generalization, and in particular modeloriented generalization, is an important process in this context, because it enables translation between different levels of precision. This paper provides a formal approach to multi-resolution in spatial data handling. It begins by motivating the work and pointing to some of the background research, and then introduces the basic concepts underlying the approach, focusing on the new concept of a stratified map space. The approach is quite general, and to show its application, the paper uses it to provide a formal foundation for generalization and vague regions. Keywords: resolution, generalization, vagueness, theory 1. Introduction W...

. This work is a contribution to the developing literature on multi-resolution data models. It considers operations for model-oriented generalization in the case where the underlying data is structured as a graph. The paper presents a new approach in that a distinction is made between generalizations that amalgamate data objects and those that select data objects. We show that these two types of generalization are conceptually distinct, and provide a formal framework in which both can be understood. Generalizations that are combinations of amalgamation and selection are termed simplifications, and the paper provides a formal framework in which simplifications can be computed (for example, as compositions of other simplifications). A detailed case study is presented to illustrate the techniques developed, and directions for further work are discussed. 1 Introduction Specialist spatial information systems (SIS) play an increasingly important role within the Information Tech...

For a long time topological predicates between spatial objects have been a main area of research on spatial data handling, reasoning, and query languages. But these predicates still suffer from two main restrictions: first, they are only applicable to simplified abstractions of spatial objects like single points, continuous lines, and simple regions, as they occur in systems like current geographical information systems and spatial database systems. Since these abstractions are usually not sufficient to cope with the complexity of geographic reality, their generalization is needed which especially has influence on the nature and definition of their topological relationships. This paper gives a formal definition of complex crisp regions, which may consist of several components and which may have holes, and it especially shows how topological predicates can be defined on them. Second, topological predicates so far only operate on crisp but not on fuzzy spatial objects which occur frequently in geographical reality. Based on complex crisp regions, this paper gives a definition of their fuzzy counterparts and shows how topological predicates can be defined on them. 1

For the majority of spatiotemporal applications, we assume that the modeled world is precise and bound. This simplification seems unnecessary crude for many environments handling spatial and temporal extents, such as navigational applications. In this work, we explore fuzziness and uncertainty, which we subsume under the term indeterminacy, in the spatiotemporal context.

. In multi-resolution data handling, a less detailed structure is often derived from a more detailed one by amalgamating elements which are indistinguishable at the lower level of detail. This gathering together of indistinguishable elements is called a granulation of the more detailed structure. When handling spatial data at several levels of detail the granulation of graphs is an important topic. The importance of graphs arises from their widespread use in modelling networks, and also from the use of dual graphs of spatial partitions. This paper demonstrates that there are several quite different kinds of granulation for graphs. Four kinds are described in detail, and situations where some of these may arise in spatial information systems are indicated. One particular kind of granulation leads to a new formulation of the boundary-sensitive approach to qualitative location developed by Bittner and Stell. Vague graphs and their connection with granulation are also discusse...

Traditional computational models of geographic phenomena offer no room for imperfection. Underlying this tradition is the simplifying assumption that reality is certain, crisp, unambiguous, independent of context, and capable of quantitative representation. This paper reports on initial work which explicitly recognises that most geographic information is intrinsically imperfect. Based on an ontology of imperfection the paper explores a formal model of imperfect geographic information using multi-valued logic. The development of Java software able to assist with a geodemographic retail site assessment application is used to illustrate the utility of a formal approach.

The relationship between less detailed and more detailed versions of data is one of the major issues in processing geographic information. Fundamental to much work in model-oriented generalization, also called semantic generalization, is the notion of an equivalence relation. Given an equivalence relation on a set, the techniques of rough set theory can be applied to give generalized descriptions of subsets of the original set. The notion of equivalence relation, or partition, has recently been significantly extended by the introduction of the notion of a granular partition. A granular partition provides what may be thought of as a hierarchical family of partial equivalence relations. In this paper we show how the mechanisms for making rough descriptions with respect to an equivalence relation can be extended to give rough descriptions with respect to a granular partition. In order to do this, we also show how some of the theory of granular partitions can be reformulated; this clarifies the connections between equivalence relations and granular partitions. With the help of this correspondence we then can show how the notion of hierarchical systems of partial equivalence classes relates to partitions of partial sets, i.e., partitions of sets in which not all members are known. This gives us new insight into the relationships between roughness and vagueness. 1

Mechanisms for overcoming semantic heterogeneity in diverse information sources are critical components of any interoperable system. In the case of diverse geographic information sources, such mechanisms present particular diffculties since the semantic structure of geographic information cannot be considered independently of its spatial structure. This paper develops a new approach to the integration of semantically heterogeneous geographic information which is capable of addressing the spatial and thematic aspects of geographic information in concert. The approach is founded on an algebraic model of spatiothematic information layers. Variations in the thematic structure of layers are explored, including the integration of layers with taxonomic thematic structure. The effects of changes in the thematic granularity of layers are also considered. Finally, a case study of the integration of heterogeneous land cover data is used to illustrate the relevance of the formal model within a practical application.