On a Mathematical Foundation of Axiomatic

The axiomatic design approach and its two underlying postulates , the independence and the information axiom, introduced by Suh (1990) are based on the fundamental claim that \there are generalizable principles that govern the design process and that these in the form of the design axioms are general principles or self-evident truths that cannot be derived or proven to be true except that there are no counterexamples or exceptions" (adapted from (Suh, 1994)). This paper shortly describes a mathematical framework which allows replacing the independence and the information axiom with the so-called evaluation hypothesis (Rudolph, 1995a). This evaluation hypothesis is based on the technique of dimensional analysis known from physics and allows the straightforward derivation of expressions that in special cases match the above stated independence axiom. For the information axiom a diierent mathematical expression is obtained. The new theoretical approach has the advantage of possessing an epistemological foundation in form of four fundamental requirements for the evaluation model of a design object which can be motivated through a rational thought process. The two diierent model assumptions are compared, discussed and illustrated using a published axiomatic design reference example.