Abstract
Firstly, the authors analyzed the properties of primary-onditionals and secondary-conditionals, establish the minimum system C2Lm of primary- conditionals and secondary-conditionals, and then prove some of the formal theorems of the system which have important intuitive meanings. Secondly, the authors constructed the neighborhood semantics, prove the soundness of C2Lm, introduce a general concept of canonical model by the neighborhood semantics, and then prove the completeness of C2Lm by the canonical model. Finally, according to the technical results of the minimum system C2Lm, the authors discuss some of the important problems concerning primary-conditionals and secondary-onditionals.
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