We show that any regular pseudocomplemented Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra determined by a tolerance induced by an irredundant covering.

Traditional expert systems for fault diagnosis have a bottleneck in knowledge acquisition, and have limitations in knowledge representation and reasoning. A new expert system shell for fault diagnosis is presented in this paper to develop multiple knowledge models (object model, rules, neural network, case-base and diagnose models) hierarchically based on multiple knowledge. The structure of the expert system shell and the knowledge representation of multiple models are described. Diagnostic algorithms are presented for automatic modeling and hierarchical reasoning. It will be shown that the expert system shell is very effective in building diagnostic expert systems.