Abstract In recent years two classes of knowledge structures received particular attention. They are, respectively, forward-graded and backward-graded knowledge structures. Their importance is related to the fact that the basic local independence model applied to such structures turns out to be locally unidentifiable. Spoto et al. (2012) established some sufficient conditions for a skill multimap to delineate forward- and/or backward graded knowledge structures. Drawing upon some of the theoretical results contained in that article, the present theoretical note aims at providing necessary and sufficient conditions for a skill map to delineate a forward- and/or backward graded knowledge structure.

中文翻译：

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从技能地图描绘前向后向知识结构的充要条件

摘要 近年来，两类知识结构受到特别关注。它们分别是前向分级和后向分级的知识结构。它们的重要性与这样一个事实有关，即应用于此类结构的基本局部独立模型在局部无法识别。斯波托等人。(2012) 为技能多图建立了一些充分条件，以描绘向前和/或向后分级的知识结构。借鉴该文章中包含的一些理论结果，本理论说明旨在为技能图提供必要和充分的条件，以描绘向前和/或向后分级的知识结构。