Abstract: Abstract: In this paper we suggest a modal logic system which is better to simulate the commonsense reasoning of persons. The system is constructed on the generalized kripke semantics. In the system we introduce modalities □. ◇ and ??. △, modal sentences □A, ◇A and ??A,△A. They mean A is persistent, A is accidental and A is experiential, A is precedent, respectively. Also, we prove the soundness, consistency and completeness of the system.