The design process of artifacts is first formulated based on the concepts of structure, property and function, then a new mathematical definition of specification is given. Under this formulation, the design problem is defined as an inverse of the mapping from the structure set to the specification set. Next, the design procedure of human designers is considered to be composed of an iteration of the processes of a new structure generation, computations (or experiments) of its function through the forward mapping and the comparison of this function with given specification. The role of this structure generation and comparison is interpreted as an emergent property in the design problem formulated above, and this role is relpaced by emergent computings. Finally, genetic algorithms are applied for two examples; the first one is a synthesis of passive linear filters using inductors and capacitors as elements, and the second is a synthesis of moving multi-link robots using rotating joints and links as elements. These two trials show an emergence of desiable structures and function adapting to a specification and an environment.

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