Abstract This paper introduces the bi-separability of items in knowledge structures as a bidirectional separability of items. Let ( Q , K ) be the knowledge structure delineated by the skill multimap ( Q , S , μ ) . This paper gives some necessary and sufficient conditions, expressed in terms of competencies of μ , ensuring that ( Q , K ) is discriminative (resp. bi-discriminative), which generalizes the discussion of the separability of items in the delineated knowledge structure from skill maps to skill multimaps. As applications of these results, the separability and the bi-separability are discussed around distributed skill functions and the meshing of the delineated knowledge structures.

中文翻译：

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关于技能多图描绘的知识结构中项目可分离性的说明

摘要 本文将知识结构中项目的双向可分性介绍为项目的双向可分性。让 (Q, K) 是技能多图 (Q, S, μ) 所描绘的知识结构。本文给出了一些充要条件，用 μ 的能力表达，确保 (Q , K ) 具有判别性（resp. bi-discriminative），概括了所描述的知识结构中项目与技能的可分离性的讨论。映射到技能多图。作为这些结果的应用，围绕分布式技能函数和所描绘的知识结构的网格讨论了可分离性和双可分离性。