Systems of definitions to represent dependencies between graphical elements were first exploited by Brian and Geoff Wyvill many years ago (see e.g. ). Similar principles have been applied to knowledge representation in CAD support systems  and advanced geometric modelling applications such as scientific visualisation . Our well-established programme of research at Warwick, The Empirical Modelling Project, has involved an in-depth study of the application of such definitive (definition-based) principles in modelling and programming with particular reference to interactive graphics and CAD [1, 3, 4, 8, 9]. The recent release of a public-domain version of our tkeden interpreter represents a milestone in our project, and a crucial stage in our development of these principles. Within the tkeden environment, there are rich possibilities for interacting with definitive scripts through redefinition of variables, and for constructing systems of interacting agents. The possibilities for generating and managing scripts and agents within the system are on the other hand more limited, and are represented by a range of features that are not well integrated into the framework of our current abstract computational model the Abstract Definitive Machine . Informally, our exploitation of definitive scripts and agency is inhibited by a relative lack of support for forms of hierarchical abstraction.
This paper gives a brief review of the current status of our Empirical Modelling principles and tools, and explains how these can be extended to accommodate higher-order observations and definitions. Some examples are used to illustrate how higher-order definitions can be exploited in graphics and animation. The implications of higher-order abstractions for interaction and agency, their significance in the Empirical Modelling process, and the prospects for effective implementation in a novel architecture are also discussed.