On the Closure of Generation Processes of Implication Functions from a Conjunction Function

摘要

In this paper, we focus on three generators of implication functions from a conjunctive function and a generator of a conjunction function from an implication function. The closure of the generation processes based on the three implication gerators and the conjunction generator is shown when the original implication (resp. conjunction) operator is upper (resp. lower) semi-continuous. More concretely, it is proved that at most 12 logical functions (implication and conjunction functions) are generated.