The diagnosis method for a weak-fault model with only normal behaviors of each component has evolved over decades. However, many systems now demand a strong-fault models, the fault modes of which have specific behaviors as well. It is difficult to diagnose a strong-fault model due to its non-monotonicity. Currently, diagnosis methods usually employ conflicts to isolate possible fault and the process can be expedited when some observed output is consistent with the model’s prediction where the consistency indicates probably normal components. This paper solves the problem of efficiently diagnosing a strong-fault model by proposing a novel Logic-based Truth Maintenance System (LTMS) with two search approaches based on conflict and consistency. At the beginning, the original a strong-fault model is encoded by Boolean variables and converted into Conjunctive Normal Form (CNF). Then the proposed LTMS is employed to reason over CNF and find multiple minimal conflicts and maximal consistencies when there exists fault. The search approaches offer the best candidate efficiency based on the reasoning result until the diagnosis results are obtained. The completeness, coverage, correctness and complexity of the proposals are analyzed theoretically to show their strength and weakness. Finally, the proposed approaches are demonstrated by applying them to a real-world domain—the heat control unit of a spacecraft—where the proposed methods are significantly better than best first and conflict directly with A* search methods.