Thus the opportunity to have discussionswith experts in the psychological and geographical aspects of the subjectwould be valuable for the development of my own work. The need for formalism Formal models, using mathematical concepts, are applicable to the concernsof the workshop for a number of reasons. These models are important ifwe take a computer science viewpoint and consider the construction of GISwhich take account of cognitive models. As an example, take the issue ofstructure in cognitive maps. If we want toimplement GIS in a way consistent with a user's internal cognitive map,concepts such as ordered trees or semi-lattices can be used to structurethe overall design of the system.
Formal models are also relevant to thegeographical and the psychological viewpoints.
The use of formalisms whenbuilding cognitive models of dynamic phenomena allows us to understandrelationships between a variety of proposed models, and to assess the relativemerits of different models. Aspects of Change There are several relatively recent developments in mathematics which canplay a role in modelling cognitive aspects of change. Rather than attemptto catalogue everything which might be useful, I want to consider threetopics. To understand how these topics relate to each other, and to thenotion of change itself, I will first consider three aspects which areoften present when dealing with phenomena of change. The development of a city over an historical period provides a simpleillustration.