Abstract. This article considers the philosophical and experiential foundations of human perception of geographical phenomena and their abstraction and coding in geographical information systems. It examines the role of culture and language in describing geographical reality and explores the ways geographical data models reflect how people view the world. Differences between those who see the world as made of exact entities and smooth continuous surfaces, and those who prefer to view reality as a dynamic and complex are explored in terms of five aspects of spatial data, namely (i) objects versus fields, (ii) single scale versus multiple scales, (iii) Boolean versus multivalued logic, (iv) static versus dynamic descriptions and (v) determinism versus uncertainty. These five aspects are further divided into nine factors of geographical data which indicate the differences in the way people perceive spatial data. Eight “typical” GIS applications and four generic methods of handling spatial data are examined in terms of these nine factors to define a GIS “hyperspace”. The locations of the typical applications and the generic methods in this hyperspace show why no single generic approach to spatial data handling is sufficient for all possible applications. The analysis reinforces the authors' contention that spatial data analysis tools need to be chosen and developed to match the way users perceive their domains: these tools should not impose alien thought modes on users just because they are impressively “high tech”. The implications of this conclusion for choosing or developing spatial information systems, for data standardization and generalisation and for the further development of “GIS” as a discipline in its own right are presented as topics for further discussion.

Abstract: Practical needs in the realm of Geographic Information Systems (GIS) have driven the efforts to investigate formal and sound methods to describe spatial relations. After an introduction of the basic ideas and notions of topology, a novel theory of topological relations between sets is developed in which the relations are defined in terms of the intersections of the boundaries and interiors of two sets. By considering empty and non-empty as the values of the intersections, a total of sixteen topological spatial relations are described, each of which can be realized in RxR. This set is reduced to nine relations if the sets are restricted to spatial regions, a fairly broad class of subsets of a connected topological space having application to GIS. It is shown that these relations correspond to some of the standard set-theoretic and topological spatial relations between sets such as equality, disjointness, and containment in the interior.

The framework is independend of the existence of a distance function.

Abstract: Over the last ten years, a subfield of GIScience has been recognized that addresses the linkage between human thought regarding geographic space and the mechanisms of implementing these in computational models. This research area has developed an identity through a series of successful international conferences and the establishment of a journal. It has also been complemented through community activities such as an international standardization efforts and GIS interoperability. Historically, much of the advancement in computational methods has occurred at - or close to - the implementation level, as exemplified by the attention on the development of spatial access methods. Significant progress has been made at the levels of spatial data models and spatial query languages, although we note the lack of a comprehensive theoretical framework comparable to the relational data model in database management systems. The difficult problems that need future research efforts are the highly abstract level of capturing semantics of geographic information. A cognitive motivation is most promising as it shapes the focus on the user's needs and points of view, rather than on efficiency as in the case of a bottom-up system design. We also identify the need for new research in fields, models of qualitative spatial information, temporal aspects, knowledge discovery, and the integration of GIS with database management systems.

A spatial join takes two sets of spatial objects as input and produces a set of pairs of spatial objects as output, such that each pair fulfils the given spatial predicate. Examples include, “Find all houses that are less than 10Km from a lake” or “Find all buildings that are located within a wetland.”

Early proposals for multidimensional data structures, such as k-d tree or quadtrees, focused on memory-resident data and, therefore, do not take secondary storage management explicitly into account.

The focus of GIS has to rely on cognitive considerations, rather than making small increments to established algorithms and data structures.

Abstract: The application of traditional database query languages, primarily the SQL, for GIS and other non-standard database applications has been tried unsuccessfully, therefore, several extensions to the relational SQL have been proposed to serve as a spatial query language. It is argued that the SQL framework is inappropriate for an interactive query language for GIS and an extended SQL is at best a short term solution. Any spatial SQL dialect has a number of serious deficiencies, particularly the patches to incorporate the necessary spatial concepts into SQL.

A criterion for evaluating the suitability of a query language for a non-standard application domain is: “How useful are the database operations provided by the query language for the particular application?”

Abstract:The tool we use influences the product. This paper demonstrates that higher order functions are a necessary tool for research in the GIS area, because higher order functions permit to separate the treatment of attribute data from the organisation of processing in data structures. Higher order functions are functions which have functions as arguments. A function to traverse a data structure can thus have as an argument a function to perform specific operations with the attribute data stored. This is crucial in the GIS arena, where complex spatial data structures are necessary. Higher order functions were tacitly assumed for Tomlin’s Map Algebra. The lack of higher order functions in the design stage of GIS and in the implementation is currently most felt for visualization, where the problems of the interaction between the generic computer graphics solutions and the particulars of the application area preclude advanced solutions, which combine the best results from both worlds. Similar problems are to be expected with the use of OpenGIS standardized functionality. This paper demonstrates the concept of higher order functions in a modern functional programming language with a class based (object-oriented) type concept. It shows how the processing of data elements is completely separated from the processing of the data structure. Code for different implementations of data structures can be freely combined with code for different types of representation of spatial properties in cells. The code fragments in the paper are executable code in the Gofer/Haskell functional programming language.

In C++ a special ‘iterator’ concept is provided (but tricky to use) to save the programmer the difficulties with passing functions as parameters. The programming languages used for implementation are based on variables and statements and functions remain second class citizens.

higher order functions allow to separate the part of operations specific to the data structure from the code of the operations which is specific to the data type stored. GIS are large data collections and must use complex spatial data structures. It is beneficial to separate the code which traverses the data structure from the code which operates on the feature data.

Abstract: We argue that the basic typology of spatial boundaries involves an opposition between bona fide (or physical) boundaries on the one hand, and fiat boundaries on the other, the latter being exemplified especially by boundaries induced through human demarcation, for example in the geographic realm. The classical metaphysical problems connected with the notions of adjacency, contact, separation and division can be resolved in an intuitive way by recognizing this two -sorted ontology of boundaries. Bona fide boundaries yield a notion of contact that is effectively modeled by classical topology; the analogue of contact involving fiat boundaries calls, however, for a different account, based on the intuition that fiat boundaries do not support the open/closed distinction on which classical topology is based. In the presence of this two -sorted ontology it then transpires that mereotopology— topology erected on a mereological basis—is more than a trivial formal variant of classical point-set topology.