On the Relations between Spatial Concepts and Geographic Objects

In processing knowledge about spatial situations, spatial concepts are employed for representing objects, properties, and relations in the world. This article presents some fundamental difficulties encountered in representing and processing knowledge about the real geographic world and motivates the need for sophisticated conceptual structures for dealing with spatial knowledge. Consequently, semantic and structural aspects of spatial concepts are discussed. Specific attention is paid to relations among different concepts on one hand and to the relation between conceptual structures and structures in the real world on the other hand. Issues like discrete vs. continuous, crisp vs. fuzzy, fine vs. coarse, and top-down vs. bottom-up concept formation are discussed in the context of spatial representations. The article derives suggestions for task-specific concept formation for the use in future Geographic Information Systems. It concludes with a discussion about fuzzy boundaries of geographic objects. 1 Why is it Difficult to Represent Geographic Knowledge? The geographic world surrounding us is extremely complex. When we want to master a given problem in this world, we need to single out particular aspects of current interest from this multifaceted formation. So at any given time we are only interested in few objects, and concerning these objects again we are regarding only particular properties and/or relations. The capability of isolating the relevant aspects and relating them to one another, results in a unique intellectual efficiency. This efficiency, however, is necessary for successfully operating in the world. To represent knowledge about the world is to make explicit specific aspects of the world. In making explicit certain aspects we ignore others. In representing knowledge, every single aspect of interest can be represented separately. Alternatively, we can aim at representing different aspects within a single structure; this requires that the different aspects of interest must be compatible, i.e., they must fit into one reference system corresponding to a global view. It is ON THE RELATION BETWEEN SPATIAL CONCEPTS AND GEOGRAPHIC OBJECTS 2 impossible to make all potentially interesting aspects of the world simultaneously explicit within one representation medium – be it a conventional map or a single representation structure in a computer. 1.1 The need for different world views There is an information-structural reason why a unified representation of the geographic world is not sufficient for solving all the tasks that can be solved with that information: we are dealing with geographic objects and with relations between these objects. If we could decide once and for all which entities we should view as objects and which as relations, our task would be simpler; however, an important feature of using world knowledge intelligently is the ability to switch between views; depending on the specific task to be solved, certain entities may be viewed as objects (fixed background entities) and others become the relations we manipulate. For other tasks, these roles may change. For example, we may consider roads as relevant geographic objects in some context. For solving certain navigation or transport tasks, we may be interested i n the intersections between these roads; having roads as objects, intersections naturally can be viewed as (connection-) relations between roads. For designing road systems, it may be convenient to view road intersections as the primary objects; the roads then can be viewed as (connection-) relations between these intersections. Of course we could say, we want to view both, roads and their intersections, as objects to obtain a unified representation (after all, our toy train systems contain both, regular tracks and switches as objects). But this does not really solve the general problem: when we view both, the roads and their intersections as (separate) objects, we create a situation in which the roads do not meet the intersecting roads; all the roads meet intersections. To solve navigation tasks, for example, we will have to consider relations between roads and intersections; thus we only have shifted the problem to the next level. W e encounter similar situations when we consider regions and their boundaries, which may be viewed as objects and relations, respectively, or vice versa. Therefore, if we want to make all potentially interesting knowledge accessible, we must make it explicit in different structures (maps or computer representations). Creating many different structures for representing knowledge about the same domain becomes expensive – both computationally and in terms of storage, since a lot of implicit information must be carried along to link the knowledge to its domain. 1.2 The GIS forms the mediating instance between world and user When developing a Geographic Information System (GIS), we must find an adequate compromise between two extreme possibilities: (1) acquiring and storing all knowledge from raw information once and for all before the knowledge is accessed, and (2) providing unprocessed raw information and computing specific knowledge on demand. On one hand we expect a GIS to contain sufficient data about the geographic world, on the other hand we want to ON THE RELATION BETWEEN SPATIAL CONCEPTS AND GEOGRAPHIC OBJECTS 3 obtain a selective view of the relevant aspects and to hide any other data of lesser interest. The entities represented in a GIS stand for the real world objects and their properties. From this point of view, GISs form the mediating instance between world’s reality and the way humans interact with this reality. The user expects the entities represented in the system to show the same properties as the real objects they are standing for. 1.3 Focus on human use of spatial knowledge The human capability of seeing the world as an inexhaustible origin of information may make it desirable to process the knowledge about the world i n such a way that it is instantly available to the human user. But if we process this knowledge about the world in advance, we will create many structures which most likely will never be accessed. On the other hand, if we do not provide structured knowledge to the user, great efforts may be required to compute this knowledge when needed. When we consider human capabilities of dealing with geographic information we can identify two challenges for the development of “intelligent” geographic information systems: (1) How can we model the human ability to focus on relevant information when solving a problem? and (2) How can we overcome the problem that a GIS can not contain all facts about the real world that might become important in a special context? 2 What are Spatial Concepts? When we consider real world objects, we usually are interested in certain properties of these objects, i.e., we regard the objects under certain aspects. For example, when we take a look at a geographic entity, say a lake, we regard it with respect to horizontal extension, depth, shape, or the like. All these notions that describe spatial aspects of a subset of the world, we call spatial concepts. We will use the term ‘concept’ in a rather general sense (c.f. [Church 1956]). Concepts can be anything we have a notion of; thus, “size” can be a concept and “big” can be a concept as well. As we predicate aspects of objects using concepts, it is obvious that spatial concepts will play a crucial role for representing knowledge about the geographic world. 2.1 Properties of spatial concepts In the following subsections we will present several semantic and structural aspects of spatial concepts which are of particular importance for their representation and for the operations that are to be performed on them. Specifically, we will address the relationships between different concepts and the relationships between concepts and real world entities. ON THE RELATION BETWEEN SPATIAL CONCEPTS AND GEOGRAPHIC OBJECTS 4 2.1.1 Concepts have meaning wrt. objects As we have already pointed out, we use concepts to describe aspects or properties of objects. This means, concepts are related to the aspects of the objects that are described. It is impossible to describe qualities of objects without using related concepts. Conversely, concepts have their meaning rooted in their relation to objects, e.g. the concept of a square is related to quadrilateral objects whose sides have equal length and meet at right angles. The mutual relatedness between concepts and objects enforces certain structures upon the concepts; in particular, not every relation between concepts and objects is meaningful. 2.1.2 Concepts have meaning wrt. other concepts Nevertheless, the meaning of spatial concepts is not only given by their relations to physical objects. The meaning of concepts is given to a large extent by their relations to other concepts (c.f. “lateral thinking” [de Bono 1969]). We illustrate this point using the example of the square: we can view the meaning of the concept “square” by its relation to all existing physical objects of square shape; but we also can view the meaning of “square” by relating it to imagined or imaginable objects of square shape. Rather than viewing the meaning to be made up of an infinite number of relationships with imaginable objects, we can view the meaning to consist of a finite number of relationships between related concepts. For example, the concept “square” may be related to the concept “rectangle” by a “special_case” relationship, to the concept “equilateral triangle” and “rhombus” by a “near_miss” relationship, to the concept “shape” by an “isa” relationship, etc. In this way, spatial concepts may have a meaning without reference to physical instances. In particular, spatial concepts have a meaning independent of an envisioned physical materialization: the shape concept “square” abstracts from the instantiation by a section of a checkers board or a marke