Logic of primary-conditionals and secondaryconditionals

Abstract

Firstly, the authors analyzed the properties of primary-onditionals and secondary-conditionals, establish the 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-conditionals.

Keywords

logic of conditionals, primary-conditionals and secondary-conditionals, neighborhood semantics, canonical model, monotonicity