The knowledge-acquisition bottleneck obstructs the development of expert systems. Refinement of existing knowledge bases is a subproblem of the knowledge-acquisition problem. The paper presents a HEuristic REfinement System (HERES), which refines rules with mixed fuzzy and nonfuzzy concepts represented in a variant of the rule representation language Z-II automatically. HERES employs heuristics and analytical methods to guide its generation of plausible refinements. The functionality and effectiveness of HERES are verified through various case studies. It has been verified that HERES can successfully refine knowledge bases. The refinement methods can handle imprecise and uncertain examples and generate approximate rules. In this aspect, they are better than other famous learning algorithms such as ID315–18, AQ11, and INDUCE14, 19, 20 because HERES' methods are currently unique in processing inexact examples and creating approximate rules.