Abstract

The completeness of the axiomatization of contingency logic over symmetric frames has been thought of as a nontrivial job, the unimodal case of which cannot be generalized to the finitely multimodal case, which in turn cannot be generalized to the infinitely multimodal case. This paper deals with the completeness of symmetric contingency logic with unlimitedly many modalities, no matter whether the set of modalities is finite or infinite.