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The construction of Abstract Design Theory and its development

抽象设计理论的构建及其发展

基本信息

批准号：
13650068
负责人：
KAKUDA Yuzuru
金额：
$ 2.18万
依托单位：
KOBE UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

项目摘要

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.

我们利用与Barwise-Seligman通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。（完整性和健全性的证明）上述结果使我们能够通过将欲望或要求的理论的分类与实体的行为的分类之间的信息流和覆盖信息流的通道分别视为理想化的生产和设计来定义实体的概念、实体的图像、实体的功能和实体的属性，以及它们之间的关系方案。我们引入了不确定分类的概念，并提出了不确定分类的概念。基于它的设计理论，并得到了与上述类似的结果，因为我们无法处理我们知识的不完整性，因此当我们仅使用标准分类时，我们无法描述现实情况的设计理论。我们形式化了集合论ZF^±，其中包含“包含不确定性”的概念，从根本上考虑不确定性，并从ZF的一致性证明了它的一致性。我们用数学的方式描述了布鲁姆关于教育与分类学的讨论，将抽象设计理论应用于教育。我们引入了多重分类的概念，以数学和严格的方式发展了设计理论中的综合概念，并发展了关于它的信息流理论。