While Logic Based Expert System (LBES) has a merit of rapid and complete inference, it also has a defect of huge knowledge base. Hierarchical LBES (HLBES) replaces the assertion time inference of LBES with the multi-level logic minimization procedure, and it guarantees smaller knowledge base comparing with LBES. This paper has two contributions. The one is proposing so-called fact-minimization procedure which reduces not only the number of facts or measured events but also the size of knowledge base dramatically. The other contribution is application of HLBES and the proposed fact-minimization to the fault diagnosis of power system. The application is successfully performed in the example with the transmission system which takes 72 goals and 352 facts.