Abstract Structures in Spatial Cognition

Structures in Spatial Cognition Christopher Habel and Carola Eschenbach University of Hamburg Abstract. The importance of studying spatial cognition in cognitive science is enforced by the fact that the applicability of spatial concepts and spatial expressions is not limited to the spatial domain. We claim that common structures underlying both concrete, physical space and other domains are the basis for using spatial expressions, e.g., prepositions like between, with respect to space as well as time or other domains. This claim opposes the thesis that the common use is based upon an analogy between concrete space and other domains. The development of geometry from Euclid’s Elements to more differentiated systems of diverse geometries and topologies can be perceived of as an example of the transfer from modeling concrete space towards describing abstract spatial structures. The importance of studying spatial cognition in cognitive science is enforced by the fact that the applicability of spatial concepts and spatial expressions is not limited to the spatial domain. We claim that common structures underlying both concrete, physical space and other domains are the basis for using spatial expressions, e.g., prepositions like between, with respect to space as well as time or other domains. This claim opposes the thesis that the common use is based upon an analogy between concrete space and other domains. The development of geometry from Euclid’s Elements to more differentiated systems of diverse geometries and topologies can be perceived of as an example of the transfer from modeling concrete space towards describing abstract spatial structures. 1 The Current Interest in Spatial Cognition: Spatial Representations and Spatial Concepts Human behavior is anchored in space and time. Spatial information, i.e., information about spatial properties of the entities in our environment, about spatial constellations in our surrounding, and about the spatial properties and relations of our bodies with respect to this surrounding, has a central position for human cognition. In the recognition of objects and events by different sensory channels, i.e., in visual, haptic or auditory perception, spatial information is involved. Motor behavior, i.e., locomotion and the movement of the body, is based on such information as well. Beyond perception and motor action, some higher cognitive activities that interact indirectly with the spatial environment are coupled with spatial information, for instance, memory, problem solving and planning (cf. Eilan et al. 1993). The interaction of spatial cognition and other cognitive faculties is also exemplified by the ability to communicate information about spatial properties of the external world, especially about objects or constellations not directly perceivable (cf. Freksa & Habel 1990). The cognitive science method of investigating and explaining cognition based on computation and representation has led to increasing research activities focusing on spatial representations and processes on such representations: * Parts of this paper are based on Habel & Eschenbach (1995). The research reported in this paper was carried out in connection to the project ‘Axiomatik räumlicher Konzepte’ (Ha 1237/7) supported by the Deutsche Forschungsgemeinschaft (DFG). Thanks to an anonymous referee for comments and suggestions for improvements. Address: FB Informatik (AB WSV) and Graduiertenkolleg Kognitionswissenschaft, Universität Hamburg, Vogt-Kölln-Str. 30, D-22527 Hamburg. {habel, eschenbach}@informatik.uni-hamburg.de. • In cognitive psychology spatial concepts are basic for thinking about objects and situations in physical space and therefore the necessary constituents for the integration of the central higher cognitive faculties with sensory, motor and linguistic faculties (cf. Miller 1978, Landau & Jackendoff 1993). • In linguistics spatial concepts are discussed as basic ingredients of the – mental – lexicon; the linguistic approach of cognitive grammar – with Lakoff, Langacker and Talmy as its most influential advocates – is committed to space as the foundation for semantics and for the general grammatical system. • In Artificial Intelligence spatial concepts are the basis for developing representational formalisms for processing spatial knowledge; for example, calculi of Qualitative Spatial Reasoning differ with respect to what their primitive terms are and which spatial expressions are definable on this basis (See, e.g., Freksa 1992, Hernández 1994, and Randell et al. 1992, Schlieder 1995a, b). In the cognitive grammar approach as well as in most other discussions on spatial information the question what the basis of using the term spatial is seems to allow a simple answer: Space is identified with three-dimensional physical space. And by this, the concrete, physical space of our environment is seen as the conceptual and semantic basis for a wide range of linguistic and non-linguistic cognition. Accordingly, spatial concepts concern size, shape or relative location of objects in three-dimensional physical space. This view is based on the judgment that direct interaction with concrete, physical space is the core of our experience and therefore of our knowledge. Our spatial experience leads to groupings among spatial concepts depending on geometrical types of spatial characterizations. Examples of such groups, each of them corresponding to types of experience, are: topological concepts • based on relations between regions and their boundaries • invariant with respect to elastic transformations concepts of ordering • based on relations between objects or regions with respect to the relative position in a spatial constellation. • independent of the extensions and distances of the objects and regions in question metric concepts • include measures of distance and size of objects and regions. 1 Following Miller (1978) we assume that the conceptual structure includes different types of concepts, e.g. concepts for objects, properties and relations. In this sense, spatial relations like touching or betweenness correspond to relational concepts, while shape properties like being round or angular correspond to predicative concepts. 2 See, e.g., Lakoff (1987), Langacker (1986), Talmy (1983). Note that in the initial phase of this framework the term space grammar was used (Langacker 1982). 3 Although it is often claimed that physical space is not concrete but an abstraction based on spatial properties and relations of material bodies, we will use the term concrete space to refer to physical space in contrast to abstract spatial structures referring to less restricted structures (such as topological, ordering or metric spaces) underlying physical space. Aspects of this division are reflected by the contrast between qualitative and quantitative spatial reasoning. The means of qualitative spatial reasoning are in many cases restricted to topological terms (e.g., Randell et al. 1992) and terms of ordering (e.g., Schlieder 1995a, b). An independent dimension of analysis concerns the distinction between concept types and types of spatial entities: On the one hand we deal with spatial relations between objects, their location or relative position. Characteristically these relations are independent of shape and extension, such that they can apply to points idealizing the place of the objects. On the other hand we are concerned with shape properties of extended objects or regions independent of their location. Shape properties are coined by the relative position of object parts among themselves. Concepts of object orientation combine both, shape of extended entities and spatial relations of their parts and other objects. These types of spatial concepts can be subdivided according to the dimension of geometrical type. As a third dimension in classifying spatial concepts, we distinguish between static and dynamic concepts. Whereas the former concern properties and relations without consideration of time and change, the latter reflect the possibility of changes of spatial properties and relations over time. Since trajectories or paths of locomotion processes are extended spatial entities, spatial concepts are applicable to them as well as to material or geographical entities. (See Table 1 for an exemplification of some sections according to the three-dimensional classification scheme).