Domain理论是数学与计算机科学交叉领域的重要研究课题之一，为函数式程序语言提供指称语义模型。信息系统为Domain提供逻辑表示。本项目拟结合模糊集理论、范畴论与形式概念分析理论，以几类重要Domain结构及其相应的信息系统为研究对象，系统地建立它们的Chu空间和概念格表示理论，具体研究内容包括：（1）通过对Chu空间中新的概念表现形式的研究，寻找与代数domain、连续domain等价的特殊Chu空间范畴；（2）研究特殊Chu空间范畴的极限、余极限和指数对象，揭示这些范畴的笛卡儿闭性；（3）研究Chu空间所诱导的信息系统，建立信息系统的Chu空间表示；（4）在范畴层面实现代数偏序集和代数的条件方向完备偏序集的Chu空间表示。（5）研究代数格的模糊化，建立模糊代数格与模糊逼近概念格之间的内在联系。本项目的研究将为Domain理论的应用提供更坚实的理论基础。

As an important interdisciplinary field of mathematics and computer science, Domain theory provides a mathematical foundation for specifying denotational semantics of functional programming languages. Information systems provide logical representations for domains. Applying fuzzy set theory, category theory and formal concept analysis theory, this project tries to establish the representation theory of several kinds of domains and their associated information systems based on Chu spaces and concept lattices. The contents include: (1) Through the study of new concept patterns in Chu spaces, present those special categories of Chu spaces which are equivalent to the categories of algebraic domains and continuous domains; (2) Study the constructions of the limits, co-limits and exponential objects in special categories of Chu spaces and consequently reveal whether they are Cartesian closed; (3) Study the properties of the information systems induced by special Chu spaces and establish the equivalence between their associated categories; (4) Explore the properties of sub-structures of special Chu spaces and finally provide the representation of algebraic posets and algebraic conditionally up-complete posets; (5) Fuzzify the algebraic lattices and discuss the relation between fuzzy algebraic lattice and fuzzy approximate concept lattices. The study will provide a more solid foundation for the applications of Domain theory.