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Knowledge space theory (KST) is a mathematical framework for the assessment of knowledge and learning in education. An important task of KST is to achieve all of the atoms. With the development of KST, considering its relationship with formal concept analysis (FCA) has become a hot issue. The atoms of the knowledge space with application in knowledge reduction based on FCA is examined in this paper. The knowledge space and its properties based on FCA are first discussed. Knowledge reduction and its relationship with molecules in the knowledge context are then investigated. A Boolean matrix is employed to determine molecules and meet-irreducible elements in the knowledge context. The method of the knowledge-reduction-based Boolean matrix in the knowledge space is also explored. Furthermore, an algorithm for finding the atoms of the knowledge space in the knowledge context is developed using a Boolean matrix.

A New Approach of Knowledge Reduction in Knowledge Context Based on Boolean Matrix