中文摘要：

概念格理论中的G-D基是一个形式背景的最小蕴涵基，从G—D基中可以产生一个背景的所有蕴涵，对G-D基的研究对于数据挖掘和规则提取都有很重要的意义。当G—D基中的蕴涵很多时，从它推导出背景中的全部蕴涵就很困难，减小G—D基的尺寸能够节省很多时间。提出了利用概念层次图约简G—D基的尺寸，通过利用Armstrong公理系统比较说明了G—D基的尺寸变小后推导蕴涵的效率明显提高，并提出了恢复G—D基中的蕴涵的一种并行算法，该算法基于可约属性类对G—D基中的蕴涵进行恢复。

英文摘要：

G-D base is the minimum implication base of a formal context in concept lattice theory, all of the implications of the context can be generated from G-D base. Research on G-D base has an important meaning for data mining and associations refining. When many implications exist in G-D base, it will be very difficult to deduce all the implications of the context from it. Reducing the size of G-D base can save lots of time. This paper presented reducing the size of G-D base by using concept layer graph, the efficiency of deducing implications from G-D base whose size reduced had an obvious improvement compared to the original G-D base with Armstrong＇ s axiom system, and presented a collateral method to restore the implications in G-D base. All the implications in G-D base can be restored based on the reducible attributes classes with this method.