Axiomatic Theory of Design Modeling

In this paper, an axiomatic theory is established for studying design. Using this theory, a formal model of design is derived to represent the syntactic structure of hierarchical evolving design objects and the dynamic design process. The axiomatic theory can be used by design theorists and computer scientists as a formal logical tool to model design whereas the derived formal model can be used by designers to organize their design activities and by software developers to implement various CAD systems. The axiomatic theory includes two groups of axioms: axioms of objects and axioms of the human thought. They address the character of two central entities in the design process: nature and the human thought. Two important notions derived from the axioms are structure and range operations, which naturally represent basic thought processes, such as aggregation and generalization, in the design process. Related work is reviewed to show the history of the axiomatic approach to the modeling of design. Future directions are also given.