The construction of Abstract Design Theory and its development

本文利用与Barwise-Seligman信道理论中的信息态射不同的条件态射概念，直接定义了信息流的概念，并证明了它们是等价的。(The完整性和可靠性的证明）上述结果允许我们定义实体的概念、实体的图像、实体的功能和实体的属性，以及它们的关系的方案，通过将期望或需求理论的分类与实体的行为的分类之间的信息流以及覆盖信息流的通道视为理想化的产品，我们引入了不确定分类的概念，并在此基础上发展了设计理论，并给出了与上述类似的结果，由于我们不能处理我们的知识的不完整性，因此当我们只使用标准分类时，我们不能描述现实情况下的设计理论。从根本上考虑不确定性，并从ZF的一致性出发证明了其一致性。本文通过将抽象设计理论应用于教育，以数学的方式描述了布卢姆关于教育的分类讨论。我们引入了多重分类的概念，以数学的、严格的方式发展了设计理论中的综合概念，并发展出一套关于信息流的理论。

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.