Introduction
Modeling creativity and knowledge-based creative design is a topic that invokes both positive and negative responses from designers and researchers in artificial intelligence and design. The topic is a-difficult one given our current understanding of creativity and potential computational models of creativity. For some, the notion of understanding creativity is in itself a contradiction of terms. In this chapter we raise some of the issues in proposing that creativity can be modeled and that knowledge-based approaches have the potential to provide computational models of creativity.

1.1 Creative design
Design distinguishes itself from other human activities in a variety of ways. One of the most important ways is that the resulting artifact is expected to be different, albeit even if only slightly, from previous artifacts. This places design within a social context because the differences are evaluated within that context. The magnitude and quality of these differences are commonly used to separate artifacts into two categories although the boundary between them is fuzzy and constantly changes. These two categories are labeled routine and nonroutine designs. The labels can be applied equally to the processes of design that produced them as to the artifacts or designs themselves. The interest in drawing this distinction lies in the implications it has for articulating computational processes that support design activity. The inference is that processes for routine design are likely to be different from those for nonroutine design.

Routine designs may be defined as ones that are recognized as not being different from previously produced designs in their class in any substantive way. Thus, in structural engineering, designing a reinforced concrete beam for a given span and load subject to the normal goals and constraints generally will result in a rectangular cross-section of particular dimensions with certain reinforcement sizes and placement. Whereas another designer may produce a design that has different dimensions and reinforcement sizes and placement, the two designs will be recognized as being remarkably similar. Furthermore, the same designer designing another reinforced concrete beam for another span and load may produce a design with a rectangular crosssection of different dimensions and reinforcement sizes and placement and this design is also recognized as being similar to the previous design.

What makes these designs similar, it can be argued, is that they all exhibit the same properties but with different magnitudes. More formally, we state that these designers all chose to use the same design variables to work with and produce different values for those variables dependent on their perception of the situation. They may well have used similar processes as well to produce the values of the variables. Two processes are of interest. The first is concerned with the selection of the variables of interest and the second is concerned with producing values for those variables. The design variables with their values describe a design. Nonroutine designs may be defined as ones that are recognized as being different from previously produced designs in their class in some substantive sense. We describe how we understand and interpret these differences later. It is convenient to draw a further distinction within nonroutine design. We label these two subcategories as innovative and creative design.

In innovative design we recognize that the substantive difference has come about from a particular set of values for the design variables that are outside the commonly used range. For example, in designing a camera with a zoom lens, the focal length of such lenses is normally 35 mm to 105 mm, however a designer may wish to use a range of 28 mm to 135 mm. This is likely to result in a longer, heavier lens but may well not produce any other changes. The camera would still look, feel, and work like any other similar zoom lens camera. This design could be considered innovative. A structural engineer may choose to design a reinforced concrete beam that was very deep compared to the normal depths for beams in order to emphasize the beam's load bearing function. The resulting design will not have any new design variables in it, only unusual values for those variables. However, a user of the design may evaluate it as being different from previously produced designs. In creative designs we recognize that the substantive difference has come about from the introduction of new design variables. For example, in designing telephones the normal way of allowing the user to move away from the location of a telephone cradle has been to provide a long, extensible cord connecting the handset to the cradle. The introduction of an alternate means of connection of the handset to the cradle based on radio waves produces a design that is seen as being creative.

However, for a design to be evaluated as being creative the criterion of novelty is insufficient, utility and value are also required. Assuming all designs are novel and all designs are useful because designing is a purposeful act, value remains the important distinguishing criterion in the evaluation of the creativeness of a design. It has been suggested that value is related to two ideas transformation and concentration...