形式概念分析中的布尔子结构
Boolean Substructures in Formal Concept Analysis
摘要：
已知一个（概念）格包含一个n维布尔子序当且仅当上下文包含一个n维反义词标度作为子上下文。在这项工作中，我们更密切地调查之间的相互作用，一个给定的有限的上下文和布尔子序的概念格的布尔子上下文。为此，我们定义了从上下文的子上下文集到其概念格的子序集的映射，反之亦然，并研究了它们的结构性质。此外，我们引入闭子上下文作为闭关系的一种扩展来研究给定格的所有子格的集合。
英文摘要：
It is known that a (concept) lattice contains an n-dimensional Boolean suborder if and only if the context contains an n-dimensional contra-nominal scale as subcontext. In this work, we investigate more closely the interplay between the Boolean subcontexts of a given finite context and the Boolean suborders of its concept lattice. To this end, we define mappings from the set of subcontexts of a context to the set of suborders of its concept lattice and vice versa and study their structural properties. In addition, we introduce closed-subcontexts as an extension of closed relations to investigate the set of all sublattices of a given lattice.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
