Designing and planning are complex activities that involve the restructuring and generation of new knowledge. In the context of collaborative or distributed design and planning in particular, the location, the meaning and the management of collective knowledge becomes an important problem.

In such contexts, knowledge may be represented in terms of design entities or objects that convey geometrical definitions (e.g. lines, polygons), ontological definitions and properties (e.g. "this is a wall") etc, as well as in terms of interdependencies among those diverse descriptions. Those interdependencies evolve in time due to the changing design situation, which results to the redefinition of design objects. The problem is to device ways to capture interdependencies and use them to redefine design objects according to the changing situation.

We develop a basic framework for a method that formulates/discovers interdependencies among design objects in the form of logical connectives while generates new definitions for the design objects. This allows for design knowledge to be built and represented in a temporal fashion.

The proposed method is based on the hypothesis that design objects are potentially fully connected to each other and that they can in effect be defined through their interconnections. The method used starts by defining each design object as a fuzzy set that contains to different degrees all the other objects (fuzzy sets) in a structure that resembles a fractal formation. The discovery of interdependencies among design objects is based on Kosko's subsethood theorem; by measuring distances among fuzzy sets we can define their interdependencies by means of logical connectives (such as implication, equivalence, negation etc). As the interdependencies change in time so are the definitions of objects.

This method might contribute to the development of a framework that can facilitate that acquisition and the representation of distributed knowledge within a common metalanguage. The need for parallel definition of design objects and their structure is particularly important in cases where there is no central mechanism for the specification of the design entities and hence their dependence.

This idea is also discussed in Alexiou and Zamenopoulos (2001) A Connectionist Paradigm in the Coordination and Control of Multiple Self-Interested Agents, In Proceedings of the 2nd National Conference, Input 2001: Democracy and Technologies, Italy. Download .pdf