A comprehensive knowledge system reveals the intangible insights hidden in an information system by integrating information from multiple data sources in a synthetical manner. In this paper, we present a variable precision reduction theory, underpinned by two new concepts: distribution tables and genealogical binary trees. Sufficient and necessary conditions to extract comprehensive knowledge from a given information system are also presented and proven. A complete variable precision reduction (CVPR) algorithm is proposed, in which we introduce four important strategies, namely, distribution table abstracting, attribute rank dynamic updating, hierarchical binary classifying, and genealogical tree pruning. The completeness of our algorithm is proven theoretically and its superiority to existing methods for obtaining complete reducts is demonstrated experimentally. Finally, having obtaining the complete reduct set, we demonstrate how the relationships between the complete reduct set and comprehensive knowledge system can be visualized in a doublelayer lattice structure using Hasse diagrams.
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