Diagrammatical aspects of qualitative representations of space

In this paper we demonstrate the usefulness of the diagrammatical aspects of a qualitative representation of positions in 2-D space 6]. Qualitative representations make only as many distinctions as necessary to identify objects, events, situations, etc. in a given context (identiication task) as opposed to those needed to fully reconstruct a situation (reconstruction task). While the distinctions made are expressed propositionally in form of relations, we use data structures that analogically reeect the structure of the relational domain on a higher level of abstraction. This representation allows to perform operations such as a change in point of view or the composition of relations eeciently. As a result of the extended \imagery" debate in cognitive science 8, 13] approaches to the representation of spatial knowledge tend to fall into one of the categories \proposi-tional" or \pictorial". There are several problems with these two extreme positions: The propositional approaches focus primarly on formal properties of the representation such as soundness and completeness 14]. While doing so, however, they are forced to explicitly 1 express the rich structural properties of space using propositions. Thus, basic 1 The sense in which \explicit" and \implicit" are used in this paper is diierent from the one in the \Call for Participation" for this workshop. While the latter states for example that \The power of diagrammatic representations stems from the property that they allow the explicit representation and direct retrieval of information that can be represented only implicitly in other types of representations and then has to be computed, sometimes at great cost, to make it explicit for use.", our use refers to the way the represented and the representing domains are related. Thus, while the structural properties of space must be explicitly stated in a propositional representation, they are implicitly given by the corresponding properties of the pictorial representations.