技能映射下知识空间基的矩阵算法

Matrix algorithm of knowledge base based on skill maps

技能映射在析取模式下可以完全确定一个知识空间,从而可以完全确定知识空间的基.然而,由技能映射计算知识空间再由知识空间来计算知识基,计算过程比较复杂.本文引入布尔向量的投影与知识状态的特征向量等概念,提出并证明了基于技能映射的知识空间的基的判定定理,并根据判定定理设计知识基的算法.该算法对于给定的技能映射,在析取模式下,可以跳过计算知识空间的过程,直接求出知识空间的基.在此基础上,进一步探讨技能和基之间的关系,提出并设计出极小技能集的约简算法.

In disjunctive mode,skill mapping can completely determine a knowledge space,so it can completely determine the base of knowledge space.However,it is complicated to calculate the knowledge space by skill mapping and then calculate the knowledge base by knowledge space.In this paper,the concepts of the projection of Boolean vector and the eigenvector of knowledge state are introduced,and the judgment theorem of the base of knowledge space based on skill mapping is proposed and proved,and the algorithm of knowledge base is designed according to the judgment theorem.For a given skill mapping,in disjunctive mode,the algorithm can skip the process of calculating knowledge space and directly find the basis of knowledge space.On this basis,the relationship between skill and base is further discussed,and a reduction algorithm of minimal skill set is proposed and designed.