In most of the work on probabilistic knowledge structures, no restrictions apply to the probability distribution on the collection of knowledge states. The number of parameters needed to describe this distribution can thus be very large. An exception is provided by the Simple Learning Model (SLM) in which, by means of assumptions on the learning process, the distribution is built from other parameters. However, the application of the SLM is limited to learning spaces. The present work generalizes the SLM by suggesting a method to build the state probabilities as products of the probabilities of single (or groups of) items. The construction follows from first factorizing the probability distribution into the product of marginal and conditional probabilities based on the blocks of an ordered exact cover of the item domain, and then by imposing suitable constraints on these probabilities. A specific ordered exact cover of the item domain, distinguishing minimal from non-minimal items, is shown to be of particular interest as it allows to recover the SLM and to generalize it to a wider class of regular knowledge structures.

在大多数关于概率知识结构的工作中，对知识状态集合的概率分布没有限制。因此，描述此分布所需的参数数量可能非常大。简单学习模型（SLM）提供了一个例外，其中通过对学习过程的假设，从其他参数构建分布。但是，SLM的应用仅限于学习空间。本工作通过提出一种将状态概率构建为单个（或一组）项目的概率乘积的方法来概括SLM。首先根据项目域的有序精确覆盖的块将概率分布分解为边际和条件概率的乘积，然后进行构造，然后通过对这些概率施加适当的约束。由于最小化项目与非最小化项目之间的区别，特定领域的有序确切覆盖特别受关注，因为它可以恢复SLM并将其概括为更广泛的常规知识结构。