Abstract

Firstly, the authors analyzed the properties of primary-onditionals and secondary-conditionals, establishthe minimum system $C2L_{m}$ 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 $C2L_{m}$ , introduce a general concept of canonical model by the neighborhood semantics, and then prove the completeness of $C2L_{m}$ by the canonical model. Finally, according to the technical results of the minimum system $C2L_{m}$ , the authors discuss some of the important problems concerning primary-conditionals and secondary- onditionals