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Diagnosability is an important property in the field of fault diagnosis.In this paper,a novel approach based on logical formula is proposed to verify diagnosability of Discrete event systems(DESs).CNF-FSM is defined to represent a new model for DES.Each transition in DES can be described as a clause.According to CNF-FSM,we construct a CNF-diagnoser.Based on the resolution principle and CNF-diagnoser,an algorithm is presented to test whether the failure events can be detected or not in a finite number of observable events.Our algorithm can be applied in both off-line diagnosis and on-line diagnosis.Experimental results show that our algorithm can solve the diagnosability problem efficiently.