Abstract Design Theory
Yuzuru Kakuda, Makoto Kikuchi · Annals of the Japan Association for Philosophy of Science · 2001
a logical coherency based on their current mathematical knowledge.Painters depict motifs in their soul by painting in oils.Their heart respects the principles from their tradition, their experience, and their passion.In this case, such princi ples can be very subjective and even irrational in some cases.In these phenomena, we can find information flows which associate the world of mind with the objective world in the activity of problem-solving.Abstract Design Theory is a mathematical theory of design which aims to abstract the common features from such problem-solving phenomena based on Channel Theory, a theory of information flow by Barwise and Seligman [1].Although we are living in a world filled with information flow, it is not easy to find the appropriate flow of information for our desire.A channel is a basic notion of the theory of Barwise and Seligman and it is a principal component of the medium which makes the flow of information.When we are faced with a problem, we choose a plan to solve it.Architects draw blueprints of houses before starting the construction.Programmers write programs in high-level languages, and mathema ticians construct outlines of proofs.Painters draw sketches for paintings and composers score music on sheets.All these are examples of channels for the infor mation flow in problem solving.We call these channels in problem solving medium spaces.Finding a suitable medium space for a given problem is an important factor in problem-solving activity.Abstract Design Theory intends to analyze design with functional and medium spaces from the viewpoint of information flow, and the purpose of this paper is to propose the framework of the theory.In Section 1, we analyze how we classify entities by their functions and we shall start with an example of chimpanzees' breaking nutshells.This is an example of a situation which precedes the activity of design and it will be repeatedly referred to in this paper.Definitions of classifications and state spaces, which are basic notions of Channel Theory, will be given in Section 1. Theories will be defined and discussed in Section 2. We shall introduce the concept of functional schemes in Section 3. A functional scheme is a basic diagram which relates the knowledge world and the objective world.We shall also show how a functional logic, a mathematical structure corresponding to a functional space, can be obtained from a functional scheme in Section 3. In Section 4, we will discuss medium systems which allow for the flow of information in design.The relationship between Yoshikawa's General Design Theory and Barwise and Seligman's Channel Theory was first developed in Kakuda [2].A mathematical definition of functions emerging by connections is treated separately in Kakuda [3] within the framework of Abstract Design Theory, and an application of Abstract Design Theory to filter circuit is discussed in Toyoda et al. [6].