Extended General Design Theory (2nd Report)

Metrization of Concept Space and its Application to CAD Systems

Abstract

In this paper the autors discuss the metrization of concept spaces as an extension of General Design Theory, assuming a hypothesis that the attribute concept space is compact. According to the fact that the attribute concept space is a compact Hausdorff space, we can prove a theorem stating that this space is a distance space. This theorem gives us a way to organize our knowledge about entities using some attributive measures. An example of such metrization is presented. It also enables us to measure the convergence speed of the design solution, to utilize numerical methods to find the design solution, etc. From these discussions, we can get some theoretical remarks about data description methods for knowledge based CAD systems ; our result is that the data description method for future CAD systems should be denotative or extensional rather than connotative or intensional. This can be thought to be a very important contribution of General Design Theory to establishing the concepts of such future intelligent and integrated CAD systems.