The construction of Abstract Design Theory and its development

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We defined directly the concept of information flow using the notion of conditional morphism which is different from the notion of infomorphism in Barwise-Seligman's Channel Theory, and showed that they are equivalent. (The proof of the completeness and soundness)The above result allows us to define a concept of an entity, an image of an entity, a function of an entity, and an attribute of an entity, and a scheme of their relations by regarding an information flow between a classification of a theory of desires or requirements and a classification of behaviors of entities and a channel covering the information flow as an idealized production and a design respectively.We introduced the concept of an uncertain classification, and developed design theory based on it, and showed results which is similar to the above, since we can't handle the incompleteness of our knowledge and hence we can't describe an design theory for a realistic case when we use only standard classifications.We formalized a set theory ZF^± which contains a notion "containing uncertainly" to consider the uncertainty fundamentally, and proved its consistency from the consistency of ZF.We describe Bloom's discussion on education with taxonomy in mathematical way, by applying Abstract Design Theory to education.We introduced the concept of a multiple classification to develop a concept of synthesis in design theory in a mathematical and rigorous way, and develop a theory of information flow about it.