APPROXIMABLE CONCEPTS, CHU SPACES, AND INFORMATION SYSTEMS
APPROXIMABLE CONCEPTS, CHU SPACES, AND INFORMATION SYSTEMS
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发表时间：
2006
期刊：
影响因子：
9.9
通讯作者：
Guo-Qiang Zhang;Gongqin Shen
中科院分区：
文献类型：
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作者：
Guo-Qiang Zhang;Gongqin Shen
本文试图把计算机科学中三个独立而又重要的领域：形式概念分析（FCA）、Chu空间和域理论（DT）结合起来。每个领域都有一个视角或重新表述，这有助于思想的流动和跨学科联系的探索。在其他结果中，我们表明，斯科特的信息系统中的状态的概念正好对应于FCA中的形式概念相对于所有有限的楚空间，和蕴涵关系对应于“关联规则”。此外，我们介绍了可逼近概念的概念，并表明，可逼近概念表示代数格是相同的斯科特域，除了包括一个顶元素。这一概念是Hitzler and Zhang，2004的基础，在这一工作中，形式背景上态射的新概念导致了一个等价于（a）完备代数格和Scott连续函数的范畴，以及（B）信息系统和可逼近映射的范畴。
This paper serves to bring three independent but important areas of com- puter science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of cross-disciplinary connections. Among other results, we show that the notion of state in Scott's information system corresponds precisely to that of formal concepts in FCA with respect to all finite Chu spaces, and the entailment relation corresponds to "association rules". We introduce, moreover, the notion of approximable concept and show that approximable concepts rep- resent algebraic lattices which are identical to Scott domains except the inclusion of a top element. This notion serves as a stepping stone in the recent work (Hitzler and Zhang, 2004) in which a new notion of morphism on formal contexts results in a cate- gory equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings.