To generate creative design solutions, void-finding, which refers to identifying gaps in the conceptual space, is considered effective. Previous research has proposed methods to support this process. However, the process of void-finding has not been theoretically explained, and current support methods largely rely on intuition or chance. To further improve the effectiveness of such support methods, it is essential to scientifically clarify the designers’ thinking process that leads to void-finding. To address this issue, in this paper, we propose a mathematical theory that explains the mechanism of this void-finding process. It is based on the axiomatic set theory introduced in the General Design Theory (GDT). The GDT is a mathematical theory that describes the intellectual processes of designers by explaining how they operate within their concept space. Furthermore, to validate the proposed theory, we analyze actual design cases obtained from design experiments and apply the proposed theory to the designers’ thinking process that leads to void-finding. The analysis provides insights into the underlying mechanism of void-finding and can contribute to the development of more effective support methods for void-finding in design.
MORISHIMA et al. (Wed,) studied this question.