Application of symbolic logic to the design axioms

Abstract The Design Axions have been advanced as a methodology for use in evaluating designs of products and processes. To date, however, these Axioms have been available only as an informal set of rules. In order for the relationships among these rules to be established definitively, and to facilitate the use of computers for decision-making in design, the Axioms have been expressed here with mathematical precision. This paper investigates the use of symbolic logic for this purpose. The result is that one design rule which was previously believed to be a corollary of the Independence Axiom is actually shown to have the same formal structure. Several other propositions are seen to be derivatives of the Axioms plus some mild assumptions, while still others would require incorporating other laws of nature in addition to the existing Axioms. Another important result of the research is that stating the axioms is symbolic logic suggests how they may be encoded in a logical programming language such as Prolog. An overall architecture for an axiomatics expert system is therefore presented.