ON THE COGNITIVE FOUNDATION AND ABSTRACT MEANS OF ENGINEERING DESIGNS

Abstract

Formal inference processes in all kinds of engineering designs are based on the cognitive process and means of abstraction. This paper presents a formal treatment of system design. It first discusses the differences of system designs in abstract and concrete systems. A hierarchical abstraction model of system descriptivity (HAMSD) is developed that explains the abstract levels of entities and artifacts in both the concrete world and the abstract world. The HAMSD model classifies the design of a system at five levels known as the levels of (1) analogue objects, (2) diagrams, (3) natural languages, (4) professional notations, and (5) mathematics from the bottom up. According to the HAMSD model, an architectural, functional, or behavioral design of a system should adopt a higher-level abstract means to describe the system at a given abstract level, in order to obtain more powerful descriptivity and higher accuracy. Therefore, a mechanical system may be designed by using diagrams; while an information or software system can not be precisely described by diagrams. The reason is that the former is at an abstract level lower than the descriptive means of diagrams, but not so is the latter. Applications of the above findings in dealing with complicated problems in large-scale software system designs are discussed in the context of software engineering. Real-time process algebra (RTPA) is adopted as a highly abstract means in case studies on formal methodologies of software system design and modeling for software objects and design patterns.