Abstract
Keywords: ontology, mereology, geographic kinds, entity types, GIS
First, understanding the ontology of geographic kinds can help us to understand how different groups of humans, for example different armies in a multinational coalition in time of war, exchange, or fail to exchange, geographic information.
Second, understanding the ontology of geographic kinds can help us to understand certain characteristic types of distortions that are involved in our cognitive relations to geographic phenomena. Above all, there are tendencies in the conceptualization of geopolitical entities that underlie certain forms of territorially based conflict.
Third, geographic information systems need to manipulate representations of geographic entities, and ontological study of the corresponding entity types, especially those at the basic level, will provide default characteristics for such systems.
Fourth, entity types are a central issue in data exchange standards, where a substantial part of the semantics of the data may be carried by the types that instances are assigned to (Mark 1993). Research in ontology as a basis for the development of knowledge-interchange standards has expanded tremendously in recent years (Gruber 1993). This paper is designed as a contribution to such research in the specific field of geography.
Existing research on cognitive categories has standardly addressed entities on the sub-geographic scale: manipulable entities of the table-top world, objects of roughly human scale (birds, pets, toys) and other similar phenomena. For such entities, the 'what' and the 'where' are almost always independent. In the geographic world, in contrast, the 'what' and the 'where' are intimately intertwined. In the geographic world, categorization is also very often size- or scale-dependent. (Consider: pond, lake, sea, ocean.) In the geographic world, to a much greater extent than in the world of table-top space, the realization that a thing exists at all may have individual or cultural variability. In the geographic world, too, the boundaries of the objects with which we have to deal are themselves salient phenomena for purposes of categorization. These boundaries may be crisp or graded, and they may be subject to dispute. Moreover, the identification of what a thing is may influence the location and structure of the boundary; for example, if a given topographic feature is identified as a marsh, then its boundary may be located farther up the slope than would be the boundary of the same feature if it had been identified as a lake. These are all features of categorization that are all but absent from the table-top world upon which theories of categorization have hitherto been based.
The problems with the set-theoretic model as an account of the categories used by ordinary humans in everyday situations are clear. For most such categories, and for most people, some members are better examples of the class than are others; furthermore, there is a great degree of agreement among human subjects as to what constitute good and bad examples. Rosch and others have accordingly proposed that natural kinds be seen as possessing a radial structure, having prototypes of more central or typical members surrounded by a penumbra of less central or less typical instances (Rosch 1973, 1978). Following Couclelis (1988), Mark (1989), and Mark and Frank (1996), a view along these lines will be accepted in what follows.
Geographic objects do not merely have constituent object-parts, they also have boundaries, which contribute as much to their ontological make-up as do the constituents that they comprehend in their interiors. Geographic objects are prototypically connected or contiguous, but they are sometimes scattered or separated. They are sometimes closed (e.g., lakes), and sometimes open (e.g., bays). Note that the above concepts of contiguity and closure are topological notions, and thus an adequate ontology of geographic objects must contain also a topology, a theory of boundaries and interiors, of connectedness and separation, that is integrated with a mereological theory of parts and wholes (Smith 1996). The topological structure will bring with it certain sorts of duality, thus for example dual to the distinction between the outer boundary and the interior of a geographic object is the distinction, within the surrounding container or host, between the inner boundary of this container and the exterior or hinterland beyond. Our topological ontology also must be able to cope with the fact that the very notion of 'boundary' can mean, in different contexts, either an abstract mathematical boundary--conceptualized as an infinitely thin line, plane or surface that is located in space but does not occupy (fill out) space--or a boundary zone, of small but finite thickness. Boundaries in the abstract sense are normally seen as falling within the province of standard mathematical topology. For geographical purposes, however, even within the category of abstract boundaries there are certain sorts of boundary phenomena which standard topology cannot deal with. If we cut an object--for instance a land parcel, or an island--in half, we are not left with one piece that is closed and another that is not. This is because abstract boundaries do not take up space, and thus they can be perfectly co-located one with another. To do justice to such phenomena we need to use special mereotopological theories that depart in crucial ways from standard topology (Smith and Varzi 1997).
An object is 'closed' in the mereotopological sense, if it includes its outer boundary as part; it is 'open' if this outer boundary is included rather in its complement. Ordinary material objects are in unproblematic fashion the owners of their surfaces. Where a complement meets an object of this sort, the object will be closed and the complement open (Asher and Vieu 1995). Regarding geographic objects, however, matters are not so simple. Consider the mouth of a volcano: where the hole meets its material host (the crater, a concave mass of rock and debris), the boundary of the hole is the surface of the host. Thus the boundary of the hole, there, belongs to the volcano, and not to the hole itself (Casati and Varzi 1994). Consider, however, the boundary of the hole where it is not in contact with its host: the boundary in the region corresponding to the opening of the hole where it faces up towards the sky. Where do we place the boundaries corresponding to those regions? Within the hole? Within the sky? Either choice would seem arbitrary, and a parallel situation is encountered in the case of bays facing out towards the sea. This very arbitrariness will reveal important features of geographic objects in general and of their boundaries in particular.
Ontologists since Aristotle have distinguished between two sorts of predications: categorial predications as we are here using this term (called by Aristotelians 'predications in the category of substance'): is a man, is a fish, is a lake, etc.; and accidental predications (or 'predications in the category of accident'), for example: is red, is colored, is big, is hungry. The former tell us under what category an object falls. They tell us what an object is. The latter tell us how an object is, per accidens, at a given moment; thus they pertain to ways in which instances of the relevant categories change from occasion to occasion.
There is no term for 'big dog' or 'small dog' corresponding to 'lake' and 'pond'. Why not? Because size for living objects is not usually a categorical matter but is an attribute changes over time. In contrast, instances of geographic categories characteristically do not grow or shrink (as animals do). In this case, size and shape may be matters for categorical predication. The question still remains whether lake is a basic level category in the sense of Rosch (1978). Is pond a subordinate subclass, a-kind-of lake? Or are lakes and ponds are both categories at the basic level, distinguished mainly by size? Bay and cove, mountain and hill, form similar pairs. Empirical research with human subjects will be needed to answer this and similar questions.
We assume the existence of a real world, populated by real entities occupying regions of space. Spatial regions form a relational system, comprising also containment relations, separation relations, relations of adjacency and overlap, and so on (Egenhofer and Herring 1991). We assume also the existence of a relation of being located at between things on the one hand (roads, forests, wetlands), and the regions in or at which they are located on the other (Casati and Varzi 1996).
Matters are complicated further by the fact that our cognitive representations of space may be under-defined or erroneous. They may show individual or culture-related differences. They may be refined or modified through social and cultural interactions, formal education, and dictionary definitions. Some spatial concepts may even be hard-wired into the perceptual systems in the senses and brain. Other concepts may be changed through use; thus, once a given concept is judged to correspond with a particular situation, then the specifics of that situation may modify the concept.
We assume that people think and reason by manipulating concepts; that computer programs are based on formal mathematical counterparts of relations between entities in the world; and that people use computers to learn about, understand, or make decisions about such entities. Thus, establishing the correspondences and interrelations among the different domains of spatial entities and relations is essential to the construction of geographic information systems and of other systems for reasoning about spatial entities and relations.
To fix our ideas, let us divide spatial reality into two sub-domains or strata, which can be conceived, provisionally, as partitions of space at different levels of granularity. (Conceive the two strata as laid on top of each other after the fashion of map layers, with the upper stratum comprising objects of larger scale.)
On the one hand is the microphysical stratum of spatial reality--it is spatial reality as it is dealt with in the physical sciences. It may be conceived, for present purposes, as a complex edifice of molecules. On the other hand is the mesoscopic stratum of spatial reality. This is the real-world counterpart of our non-scientific (naive, normal, everyday, lay) cognition and action in space.
This mesoscopic stratum has three different types of components:
1. Objects of a straightforwardly physical sort--such as rivers, forests, bridges--that are studied also by physics but which, as they are cognized within the mesoscopic stratum, have different sorts of properties. (This is in virtue of the fact that our naive cognition uses very little mathematics, has its own peculiar topology, and endows its objects with qualitative rather than quantitative features and with a social and cultural significance that is absent from the microphysical realm.)
2. Geographic objects like bays and promontories, which are also in a sense parts of the physical world but which exist only in virtue of demarcations induced by human cognition and action.
3. Geopolitical objects like nations and neighborhoods which are more than merely physical, and which exist only as the hybrid spatial products of human cognition and action.
All three sets of components are spatial objects. Indeed we might conceive mesoscopic entities in general as shadows cast by human reasoning and language (and by the associated activities) onto the spatial plane. All mesoscopic objects exist as parts of spatial reality as we here conceive it. This applies even to counties, land-parcels, postal districts, real estate subdivisions, air corridors, and so on.
Table-top examples tend further to reinforce a view according to which nature can be cut at its joints--that is, a view to the effect that there is a true, God-given structure, which science attempts to make precise. As we shall see, geographic categorization involves a degree of human-contributed arbitrariness on a number of different levels, and it is in general marked by differences in the ways different languages and cultures structure or slice their worlds. It is precisely because many geographical kinds result from a more-or-less arbitrary drawing of boundaries in a continuum that the category boundaries will likely differ from culture to culture (in ways that can lead to sometimes bloody conflict as between one group or culture and another).
Finally, the familiar Rosch-style examples form a family of separate categorial systems possessing simple tree structures, with each tree having little to do with the other trees. Geographic categories, in contrast, because they relate to objects intrinsically interrelated together within a single domain (called space), form categorial systems that interact to form a single structure. The mereological, topological and geometrical, organization of space thus has deep implications for the structure of our cognitive system of geographic categories.
Once fiat outer boundaries have been recognized, it becomes clear that the opposition between bona fide and fiat boundaries can be drawn not merely in relation to boundaries but in relation also to the objects that they bound. Examples of bona fide geographic objects are the planet Earth, Vancouver Island, the Dead Sea. Fiat objects include King County, the State of Wyoming, the Tropic of Cancer. There are, of course, cases of objects that ought reasonably to be classified as fiat objects whose boundaries involve a mixture of bona fide and fiat elements. Haiti and the Dominican Republic, which together occupy the Island of Hispaniola, are examples which spring to mind, but every national boundary will in course of time involve boundary- markers: border-posts, watch-towers, barbed wire fences and the like, which lend a physical aspect to what was initially an object of the fiat sort.
Mountains, hills, ridges, also a cape or point--we can all agree that they are real, and that it is obvious where the top of a mountain or the end of a cape is to be found. But where is the boundary of Cape Flattery on the inland side? Where is the boundary of Mont Blanc among its foothills?
In a world with our everyday human practices, a bay or a hill is just as real as a chair or rock. The former are real consensus fiat objects, the latter are real bona fide objects. Bona fide objects are for obvious reasons more likely to be objects of categorizations that enjoy a high degree of cross-cultural invariance. Fiat objects, in contrast, because they are inculcated into the world by cognition, are more likely to show cultural dependence.
If one needs to know where the shoreline is, perhaps in order to regulate access or trespassing, then one selects some particular stage in the tidal cycle, such as mean low tide level; this produces a fiat shoreline that is fixed and reasonably crisp, and that approximates a bona fide shoreline that moves with the waves and tides. You cannot see or touch or trip over the fiat shoreline; but the fiat shoreline is there, nonetheless, as a part of reality: if you cross it, you may be prosecuted.
Soil scientists in the field of course do not measure everywhere. They observe where the boundaries probably are, and draw them on the map, based on changes in underlying geology, in vegetation, in topography. Then they dig in the middle of each polygon, and use the results obtained in the laboratory to classify the whole polygon. It is said that soil scientists seldom sample near the boundaries, perhaps because they know that they are not really there. Fields for each soil property would be a better thing to store. The polygons with crisp boundaries misrepresent the phenomenon, but they were the best that could be done with static, printed, ink-on-paper media.
Imagine the instances of a concept arranged in a quasi-spatial way, as happens for example in familiar accounts of color- or tone-space. Suppose that each concept is associated with some extended region in which its instances are contained, and suppose further that this is done in such a fashion that the prototypes, the most typical instances, are located in the center of the relevant region, and the less typical instances are located at distances from this center in proportion to their degree of non-typicality. Boundary or fringe cases can now be defined as those cases that are so untypical that even the slightest further deviation from the norm would imply that they are no longer instances of the given concept at all.
In this fashion counterparts of the familiar topological notions of boundary, interior, contact, separation, and continuity can be defined for the conceptual realm, and the notion of similarity as a relation between instances can be understood as a topological notion (Mostowski 1983; Petitot, 1994). In the realm of colors, for example, a is similar to b might be taken to mean that the colors of a and b lie so close together in color-space that they cannot be discriminated with the naked eye. A similarity relation is in general symmetric and reflexive, but it falls short of transitivity, and is thus not an equivalence relation. This means that it partitions the space of instances not into tidily disjoint and exhaustive equivalence classes, but rather into overlapping circles of similars. This falling short of the discreteness and exhaustiveness of partitions of the type that are generated by equivalence relations is characteristic of topological structures. In some cases, there is a continuous transition from one concept to its neighbors in concept-space, as for example in the transition from lake to marsh to wetland. In other cases, circles of similars are separated by gaps (regions of concept-space that have no instances). This is so regarding the transition from, say, lake to reservoir.
Terms like 'strait' and 'river' represent arbitrary partitions of the world of water bodies. The English language might have evolved with just one term, or three terms, comprehending the range of phenomena stretching between strait and river or, in French, between détroit and fleuve. For while the Straits of Gibraltar are certainly not a river, and the Mississippi River is certainly not a strait, there are cases--such as the Detroit River and the Bosporus--that exist on the borderline between the categories. All are flat, narrow passages that ships can sail through between two larger water bodies (lakes, seas), and all have net flow through them, due to runoff, etc. Is Lake Erie really a lake, or just a wide, deep part of the river-with-five-names that is called the St. Lawrence as it flows into the sea? Well, that depends on what you mean by 'lake'.
Casati, R., and Varzi, A. C., 1994. Holes and Other Superficialities, Cambridge, MA, and London: MIT Press (Bradford Books).
Casati, R., and Varzi, A. C., 1996. The structure of spatial location. Philosophical Studies 82, 205-239.
Couclelis, H., 1988. The truth seekers: Geographers in search of the human world. In Golledge, R., Couclelis, H., and Gould, P., editors, A Ground for Common Search. Santa Barbara, CA: The Santa Barbara Geographical Press, pp. 148-155.
Egenhofer, M., and Herring, J., 1991. Categorizing Binary Topological Relationships Between Regions, Lines, and Points in Geographic Databases. Department of Surveying Engineering, University of Maine, Orono, ME.
Gruber, T. R., 1993. A Translation Approach to Portable Ontology Specifications, Knowledge Acquisition, 5(2),199- 220.
Mark, D. M., 1989. Cognitive image-schemata for geographic information: Relations to user views and GIS interfaces. Proceedings, GIS/LIS'89, Orlando, Florida, v. 2, 551-560.
Mark, D. M., 1993. Toward a Theoretical Framework for Geographic Entity Types. In Frank, A. U., and Campari, I, editors, Spatial Information Theory: A Theoretical Basis for GIS, Berlin: Springer-Verlag, Lecture Notes in Computer Sciences No. 716, pp. 270-283.
Mark, D. M., and Frank, A. U., 1996. Experiential and Formal Models of Geographic Space. Environment and Planning, B, v. 23, pp. 3-24.
Mostowski, M., 1983. Similarities and Topology, Studies in Logic, Grammar and Rhetoric, 3, 106- 119.
Petitot, J., 1994. Phenomenology of Perception, Qualitative Physics and Sheaf Mereology, in R. Casati, B. Smith and G. White (eds.), Philosophy and the Cognitive Sciences, Vienna: Hölder-Pichler-Tempsky, 387-408.
Rosch, E., 1973. On the internal structure of perceptual and semantic categories. In T. E. Moore (editor), Cognitive Development and the Acquisition of Language, New York, Academic Press.
Rosch, E., 1978. Principles of categorization. In E. Rosch and B. B. Lloyd (editors) Cognition and Categorization. Hillsdale, NJ: Erlbaum.
Simons, P. M., 1987. Parts. An Essay in Ontology. Oxford: Clarendon Press.
Smith, B., 1995. On Drawing Lines on a Map, in Andrew U. Frank and Werner Kuhn (eds.), Spatial Information Theory. A Theoretical basis for GIS, Berlin/Heidelberg/New York, etc.: Springer (1995): 475-484.
Smith, B., 1996. Mereotopology: A Theory of Parts and Boundaries. Data and Knowledge Engineering, 20, 287-303.
Smith, B., and Varzi, A., 1997. Fiat and Bona Fide Boundaries: An Essay on the Foundations of Geography, in S. C. Hirtle and A. U. Frank (eds.), Spatial Information Theory. International Conference COSIT '97. Laurel Highlands, Pennsylvania, October 1997 (Lecture Notes in Computer Science 1329), Berlin/New York: Springer Verlag, 10 3-119.