Cognitive Perspectives on

Spatial and Spatio-Temporal Reasoning

Knowledge about human cognition is important to the social and behavioral sciences because human behavior is based on the beliefs and knowledge that people have about their worlds. An understanding of human spatial cognition and reasoning will undoubtedly be useful in explaining and predicting human behavior in geographic space. It also should contribute to the development of fundamental theory in geographic information science and cognitive science. And lastly, formalizing these theoretical advances should aid in the design of improved information systems to support human decision-making in geographic space.

This essay reviews some of the aspects of spatial cognition and related topics that are most relevant to the advancement of geographic information science. It attempts to paint a broad picture of the field, admittedly from this author's perspective. Details cannot be included, but there are pointers to some key references for further reading. The essay may raise more questions than it answers, but questions are fundamental to progress in basic research.

Artificial Intelligence (AI) is a key area of Computer Science, and has been applied to geographic information in a number of ways (Couclelis, 1986; Smith, 19xx). AI is a diverse field, but two major sub-areas can be distinguished by their very different goals. The field of Expert Systems (ES) seeks to build computational systems that perform tasks formerly thought to require human intelligence. In ES, it is not necessary or even desired that the machine perform the task in the same way that humans do; although studies of human performance may lead to implementable models, other methods of designing Expert Systems also are important. In essence, the goal of ES is engineering, that is, building things that work well.

The other side of AI has more scientific objectives, attempting to explain or account for aspects of human intelligence, or of 'intelligence' in general. Normally, this side of AI uses computer implementations as a method for approaching understanding, and as a forum for formal modeling. Cognitive Science includes this kind of AI, along with related disciplines from the behavioral and social sciences.

Spatial cognition forms an important part of cognitive science. Lakoff and Johnson (1980) suggested that spatial situations form the basis or source domain for many metaphors used to structure more abstract conceptual domains. Cognitive science provides geographic information science with research methods and philosophical stances that help ground theories of spatial information and spatial cognition. Geographic information science can in turn provide cognitive science with new and perhaps more sophisticated formalisms for representing spatial entities and relations.

The role of formalism in geographic information science and cognitive science deserves some special attention. Computer programs involve formal models of the phenomena that the program is modeling or representing. Explicit formal models increase the chance that the program will behave consistently and correctly. Formal models also help in the development of theories, and in designing hypotheses to test. Formalization certainly is essential to software engineering. It also is a very important part of a cognitive science approach to spatial information and cognition. Scientific explanations go beyond formalization of the problem and its elements, and normally involve empirical evidence that supports, or at least fails to refute, theoretical statements.

Positivist approaches to explanation and understanding are based on implicit or explicit claims that the World has an objective nature, independent of human observation. Science is involved with discovering, uncovering, or revealing the inherent structure of this World. Scientists do not always agree, and thus multiple and contradictory explanations may exist for a while. However, proponents of each explanation would likely agree that only one of then can be correct. People trained in the sciences often assume that this search for refutable theoretical descriptions of the real world is the only basis for explanation and understanding. However, there are other philosophical stances that propose quite different methods of inquiry and understanding. For example, solipsism asserts that the human mind does not have direct access to the World at all—people only have 'beliefs', based on what their senses reported. In this extreme view, the World may not even exist outside our own minds.

Clearly, there is a huge gulf between objectivist and solipsist accounts of explanation. However, each view appears to have some merit. Experiential Realism is a philosophical stance that appears to bridge this gap by asserting that mental models of the World come from experience with that World. Even though the mind cannot experience that world 'directly', the indirect experiences of that World are shaped in consistent ways by the physical nature of the World, by the physical nature of our individual senses, and by the physical nature of our own bodies and how they interact physically with that world. George Lakoff introduced Experiential Realism in great detail in his 1987 book "Women, Fire, and Dangerous Things." The model is, however, well described in the much earlier book by Lakoff and Johnson (1980), and further elaborated by Johnson (1987). It appears to have strong potential as a basis for computational models of the human mind. In geography and spatial cognition, cognitive models based on Experiential Realism have been discussed in several paper (Couclelis, 1988; Mark and Frank 1989; Frank and Mark 1991; Mark and Frank 1996).

Categories form a keystone of Experiential Realism. Much of the organization we see in the World is structured by categories. Once a novel experience has been classified, we can infer a lot about it from the characteristics of the category we have placed it in. Science typically models categories using classical set theory. However, Rosch (1973, 1978) and other cognitive psychologists have shown convincingly that categories often have 'fuzzy' boundaries, cores, prototypes, best examples, internal radial structure, etc. For example, although from a technical point of view, all nine thousand species belonging to class Aves are equally birds, when people are asked to give an example of a kind of bird, the almost always give 'typical' ones such as sparrow or robin, not familiar yet atypical species such as duck or penguin. Experiential Realism includes this sort of model of categories, and can readily be applied to spatial relations and cognition as well as to geographic entity types. For reviews of these ideas in a geographic context, see Mark (1993a, 1993b), and Fisher (this volume).

As noted above, categorization is a basic human cognitive activity. Classification is also widely used in science. Classification is almost always a useful step toward understanding, even if the classes are extreme simplifications of the complexity actually present in the World or in our mental models of it. Spatial cognition is a complex field of study that has been examined by psychologists, geographers, urban planners, and many others. Aspects of spatial cognition can be classified along many dimensions or axes, and a variety of such models have been used. In this section, several different categorizations of spatial cognition are presented. The dimensions and basics of the classifications are given in more detail by Mark and Freundschuh (1995). One basic dimension for differentiation of spatial cognition is the kind or type of spatial knowledge. Another is scale or size of the environment or objects involved. And a third basis for classification is the source of spatial information, particularly which human senses are involved.

The kind or type of spatial knowledge is a fundamental basis for classification. Division of knowledge into procedural and declarative has a long history in artificial intelligence (Barr and Feigenbaum, 1982). The distinction seems to hold particularly well for geographic cognition and knowledge, although with some modification. Much of spatial reasoning is transformations among these forms.

Procedural knowledge concerns how to get around in geographic space, the information that forms the basis for navigation and wayfinding. In its most pure form, this knowledge is inaccessible to conscious introspection. However, it often can be reasoned about consciously, and we may be able to tell others how to get from place to place by accessing our own procedural knowledge of the route. But we may still be unable to estimate distances between points along familiar routes, especially by straight line distances if the route is sinuous.

Declarative knowledge is simply facts about geographic space and the entities and phenomena in it. Athens is the largest city in Greece, Maine is adjacent to New Hampshire, Strasbourg is on the Rhine, the Nile is the longest river in Africa, and Mount Everest is the highest mountain—these are all geographic facts. They may be known in relative isolation—one could know those listed above without having any idea of the distance between Athens and Mount Everest, or even which continent the latter is on.

Spatial cognition research has often presented findings about a third category of spatial knowledge, namely configurational knowledge. Configurational knowledge of a geographic space is essentially 'map-like', and includes knowledge of relative positions, distances, angles, etc. This can be treated as a special type of declarative knowledge, and certainly falls on the declarative side of the procedural/declarative dichotomy. However, it is peculiarly spatial, and thus differs from declarative knowledge of the more general type.

As noted above, scale is another basis for classifying spatial knowledge. Geometry and physics are essentially constant over a large range of spatial and temporal scales; only around the size of the individual atom and smaller, or as we approach the speed of light, do Newtonian physics and Euclidean geometry have to be abandoned in favor of newer twentieth century models. Many views of spatial cognition have naively accept this, and assumed that the 'same' models of geometry apply on the table, in the city, or over continents and hemispheres. However, it seems that human spatial concepts may vary with scale, in particular with size relative to the human body. This should be no surprise if experiential realism is more or less correct, since the human body, senses, and power to manipulate form the cognitive anchor points for the external world.

Researchers have identified several scales, or scale-based typologies of kinds of spatial knowledge. Two particular scales come out in most such analyses. One kind of space is defined by manipulable spaces and entities, roughly human-sized and smaller. These can be perceived holistically, through several senses at once, and are fundamentally three-dimensional. The other kind of space is much larger than the human body, and are normally experienced part by part during immersion within them. These are best termed geographic spaces, but also have been termed transperceptual spaces (Downs and Stea, 1977). Geographic spaces are 'assembled' in memory through spatial reasoning.

Manipulable and geographic spaces differ in a number of ways. Manipulable spaces are populated by three-dimensional entities, most of which are moveable. When they are moved, their attributes such as size, shape, and color are not expected to change. Euclidean geometry provides very good descriptions of manipulable spaces. Such spaces are often described using observer-centered references frames (left-right, etc.). Geographic spaces, on the other hand, contain many entities with indistinct boundaries. Geographic entities are normally parts of the Earth's surface, and thus not moveable. If they do 'move' (the spread of a wild fire, for example), then their attributes also are expected to change. Euclidean geometry does not seem to be natural for describing geographic spaces; traditional maps, which themselves are manipulable entities, play a key role in assembling cognitive information about geographic spaces into coherent Euclidean mental models (Lloyd, 1989; Freundschuh, 1991). Cardinal directions are often used for describing relative positions in geographic space.

There are exceptions to some of the above tendencies. For example, many people seem to have trouble using cardinal directions even in familiar outdoor spaces, yet some cultures use cardinal directions even for table-top spaces (Pederson, 1993). Montello (1993) has proposed a more elaborate subdivision of kinds of spaces based on scale. And Couclelis (1993) has suggested that the noted raster-vector 'debate' for geographic information systems may relate to the differences between manipulable spaces (entities, vector) and geographic spaces (fields, raster).

A third basis for classification is the source of spatial information, particularly which human senses are involved. Mark (1992) suggested that information based on different senses also represents a hierarchy for metaphorical structuring. Haptic spatial knowledge, acquired primarily from touch and body movement, is the most basic. This would appear to apply only in manipulable space, and is probably well developed before a child reaches the age of one year. Mark claimed that pictorial spaces, based on the remote sensing of the immediate environment, mainly through sight and sound, are conceptually structured in terms of concepts from haptic space. However, the range of pictorial space is unlimited, and is bounded only by barriers to vision and hearing that are provided by the environment. Many of the 'spatialization metaphors' discussed by Lakoff and Johnson (1980) fall into this category, or structure more abstract conceptual domains in these terms. Thirdly, the sense-based classification identified transperceptual (geographic) spaces, which are structured partly by pictures (maps, mental maps). Mark noted that while there are metaphorical links across the hierarchy defined by haptic, pictorial, and transperceptual spaces, each can also form the basis for human-computer interaction, in general as well as for GIS. Haptic concepts lead to direct manipulation interfaces, pictorial to pan and zoom metaphors, and transperceptual to wayfinding metaphors.

Having discussed some general models of spatial cognition from a 'top down' perspective, it is appropriate to turn briefly to look at some primitives or building blocks for spatial cognition. In his influential and controversial book, "The Child's Conception of Space" (Piaget and Inhelder, 1956), Jean Piaget proposed that "the perception of space involves a gradual construction and certainly does not exist ready-made at the outset of development" (p. 6). Piaget claimed that by the age of about 4-5 months, the child can recognize and reason about five spatial relations. In order from the most elementary, these are: proximity, separation, order (or spatial succession), enclosure (or surrounding), and continuity (Piaget and Inhelder, pp. 6-8). Piaget went on to relate these five to elements of Gestalt theory, and to the bases of topology, concluding that these are evidence that topology is very basic to perception and cognition (p. 9). Golledge (1995) proposed a somewhat higher-level set of primitive concepts on which models of spatial knowledge can be built. Golledge proposes that identity, location, magnitude, and time are first-order primitives, with distance, angle and direction, sequence and order, and connection and linkage as fundamental derived concepts.

Once self has been differentiated from surrounding, and the world has been divided into 'things', two topological primitives seem essential and distinct: containment and contact. These can form the basis of formal models of topological spatial relations, as has been shown by Pantazis (this volume). The 9-Intersection model of spatial relations (Egenhofer and Herring, 1994) also is based on these two, but includes just one spatial relation per se, namely intersection, and models contact as an intersection of boundaries. Another spatial primitive, part-whole decomposition, is used to divide each spatial entity into an interior and a boundary. Mark and Egenhofer (1994, 1995) have shown that this model can account for much of the variation in how subjects apply higher-level terms such as 'crosses' or 'enters' to spatial relations between roads and parks in geographic space. The use of such models for other aspects of spatial cognition and reasoning awaits further studies.

The cognitive sciences, being interdisciplinary, include a variety of methods for reaching "explanation". In a scientific approach, objective "evidence" is normally required to support theories or other explanations, but different fields favor different kinds of evidence, or different standards. Evidence can come from mathematical proofs, from successful computational implementations, from human subjects experiments, from observation of natural human behavior or its effects, from the nature and structure of natural language, through introspection, and in other ways.

One important methodological tension is between observing natural human behavior and its results, or performing experiments. Rigorous experimental control is seldom possible in the real world. Thus it is difficult to rule out the possibility that extraneous factors are influencing the results. However, well-controlled experiments in human cognition normally involve highly-simplified situations that have been abstracted from reality, and thus results may not provide convincing explanations of natural behavior. The practical question is either, how can researchers achieve control in experiments conducted in the real world, or how can they obtain measures of natural behavior in laboratory experiments. If neither of these goals can be achieved, then what are the appropriate trade-offs between control and natural behavior? These are important questions for anyone planning to design experiments with human subjects.

Human natural language can be a particularly interesting site for studying spatial cognition. Many aspects of natural language can be used to get at principles of spatial reasoning and cognition. These include the grammar and syntax of languages, the lexicons of languages and their etymologies, as well as their semantics, pragmatics, and use. All of these can provide valuable information and insights about human spatial cognition. Cross-linguistic studies are especially valuable.

The relation of language to cognition is, however, controversial. The Sapir-Whorf hypothesis asserts that people think "in" (using?) their natural language. If this is true, then it seems that the nature and structure of that language can influence thought. In an extreme form of 'Whorfianism', language determines and limits thought. More frequently, current proponents of this approach support a linguistic relativism, where certain choices of reasoning or expression are more likely for speakers of one language than for another. Many linguists, recently and notably Stephen Pinker (199x) reject any form of linguistic relativism, asserting that language is used for communicating ideas but not for formulating them. Scientific conservatism suggests that linguistic relativism should not be assumed without evidence, but design of systems based on an 'all-people-think-like-we-do' principle seems like cultural imperialism. Thus work to resolve the presence or degree of linguistic relativism in spatial relations is of high priority.

Research approaches that combine formalisms and human-subjects testing appear to be especially valuable, since each approach can enrich the other. A sound formal model promotes critical experimental design, drawing attention to which aspects of experimental stimuli should be manipulated and which aspects should be held constant. On the other hand, experimental results can indicate where the formal model needs to be elaborated and where it should be abstracted. Also, multiple modes of testing or experimental protocols, such as verbal description tasks, graphic prototypes, groupings, or agreement tasks, all should be employed, as they focus on different aspects of conceptual definitions (Mark et al., 1995).

Time is a somewhat abstract concept that is often structured both cognitively and linguistically through its relation to space. For example, most terms for temporal relations have origins as spatial prepositions or equivalents. Time and space are linked through motion, and time also manifests itself through change. Some researchers have suggested that time in geographic space is different from time in manipulable space. However, evidence for this distinction is not as clear as it is for scale-based kinds of spatial entities and spaces. Two time topics will be discussed in this section: time geography, and fictive motion.

In the 1960s, Swedish geographer Torsten Hägerstrand developed a number of theoretical models of time and process in geography. Perhaps the most famous of these models are his work on spatial diffusion processes. But another important part of Hägerstrand’s work is now known as time geography. Time geography provides a conceptual model of how time and velocity limit spatial interaction and planning. A central idea is that of the time-space 'prism' (see Figure 1). In time-geography diagrams such as this, geographic space commonly is collapsed to one dimension on the horizontal axis, and time is plotted vertically. If a person (or other object) is not moving, then a vertical line appears on the diagram. An oblique line represents motion (space and time are both changing), and the more nearly-horizontal the line is, the faster the travel. Thus, if a person has an opportunity to move in a fixed time period, but with a maximum possible speed, their movements are restricted to a diamond-shaped polygon referred to as a prism. (If space were plotted two-dimensionally with time as a third dimension, and if travel were equally fast in all directions, then such a prism would appear as a double cone.) The parts of the space-time prism that are farther from the start and end point represent places where there is less time available for non-traveling actions. An example for one person is shown in Figure 1.

The time-geography model is even more interesting in the way it exposes constraints when two or more people, based at different locations, try to meet for some joint activity. Figure 2 illustrates a hypothetical example of two people trying to meet for lunch. Although each has a two-hour lunch break, one must start and end 30 minutes earlier than the other. Thus, if they started and ended at the same place, they would have 90 minutes for the meal. The area in which the two prisms overlap (see Figure 2) represents the space-time domain in which the lunch meeting could happen, and the 'height' of the overlap zone represents the maximum duration of the lunch at each location. In this particular case, the duration for the meeting is independent of location within a fairly wide zone intermediate between the two locations from which the people start. Although the people are working less than an hour's drive apart, and each has two hours for lunch, the time-geography model indicates that they can get together for just 5/8 of an hour (about 37 minutes).

The time geography model has had important impacts on geographic thought, but usually as a conceptual model for formulating hypotheses and constraints, rather than as a empirical or computational model. Perhaps this is because methods in logic programming and inference were not widely known to geographers when the time-geography model was most popular. Time geography represents an important potential way for time to be integrated into spatial analysis for GIS, as well as a link to artificial intelligence programs for spatio-temporal reasoning. Miller (199x) reports an implementation of the time-geography model in a well-known commercial GIS.

The last point in this section regards the issue of whether space and motion might be more appropriate primitives or basic concepts than space and time. We learn in science, especially physics, that time and space (distance) are dimensional primitives (V=L/T, not T=L/V), and that velocity, motion, and change are derived properties. But does this reflect the way that people naturally think about spatial processes, and reason about space, time, and motion? Leonard Talmy has made some interesting generalizations about a cognitive and linguistic phenomenon that he calls 'fictive motion' (Talmy, 1995). In fictive motion, objects that do not move in the literal (physical) sense are talked about as if they move. A good example is "The wall runs from the ridge to the valley", which is 'fictive' (not true), because the wall does not move at all with respect to the landscape, nor was it necessarily constructed in an end-to-end sequence. Rather, our hypothetical 'gaze', or the attention of our cognition, moves along it in order to describe or understand its configuration.

Talmy has suggested that fictive motion is a language universal: every known language uses fictive motion. The pervasive use of fictive motion in human language suggests that in some ways motion may be more fundamental or basic even than space itself, never mind time. If motion is really more basic to cognition that time or space in isolation, what are the implications for spatio-temporal reasoning systems or for temporal data in GIS? It might still be best to represent space and time as separate primitives, and then infer motion, process, and change from them. Is such a choice just an implementation detail, as long as a process-based 'view' of databases and analytical models is available to users? How would we evaluate the relative advantages and disadvantages of different spatio-temporal systems? These again are fundamental research questions, being addressed in artificial intelligence, cognitive science, and geographic information science.

This essay proposes that human spatial cognition is an important topic in its own right, and also provides basic insights that are relevant to geographic models, geographic software design, and geographic information science in general. Methods from psychology, artificial intelligence, linguistics, and other parts of cognitive science can fruitfully be brought to bear on problems of cognition in and about geographic space. A philosophical position termed experiential realism seems to be a useful background for spatial cognition research, although there are alternatives. Categories are central to this model, and are a useful focus for research on cognition. Categorizations can apply to kinds of things, to attributes, to processes, or to relationships.

Spatial cognition and spatial knowledge can be categorized according to kinds of knowledge, or according to scale (size) of objects, or according to the sources of spatial information. These classifications are by no means independent, but highlight different aspects and may be relevant for different purposes. Also, primitives of spatial cognition have been identified and reviewed.

A particular point of emphasis in this essay is kinds of evidence. Both a strength and a problem for the cognitive science is the multiplicity of kinds of evidence and ways of knowing. Some people think that nothing has been established unless it has been implemented on a computer, while others feel that computer implementation is merely application. Some do not believe a conclusion unless a well-controlled experiment has been run with at least 30 subjects, whereas other rely on introspection, or on a small group of informants cultivated over months or years of participant anthropology. If alternative methods are brought to bear on the same problem, more complete answers may be revealed that convince a wider range of scientists and applications specialists.

Time is considered to be like space in some cultures and cognitive frameworks. For certain questions or models, time may be treated separately, but this can cause problems for the modeling of process and motion. Time and space combine though constraints on velocity, to limit the ranges of human activities that are possible. Time geography provides formal methods for showing how available time constrains spatial choice. Also. language often connects space and time by conceptualizing static objects as if they were moving, or moving objects as if they were static.

I believe that some key priorities for research in this area are to perform tests with human subjects to verify every assumption of the models being applied. Also, formal descriptions of all of the assumptions underlying the models or experimental designs must be given. This will allow differences in empirical results to be accounted for, and should eventually lead to unified models of the universals of human spatial and spatio-temporal cognition, and methods for highlighting individual differences and differences between human societies.

This paper is a result of research at the U. S. National Center for Geographic Information and Analysis, supported by a grant from the National Science Foundation (SBR-88-10917); support by NSF is gratefully acknowledged.