In HDL synthesis systems of EDA design tools, it often needs to be judged in high-level synthesis, RTL-level synthesis and logic-level synthesis whether a logical function is a tautology.

It is proved that modal tautologies are logically valid but not vice versa;Based on a class of continuous binary relations,the concept of quasi-tautology is introduced in fuzzy modal logic,basic properties of quasi-tautologies is obtained,and a class of tautologies and quasi-tautologies are constructed by means of theorems in the logic system ￡*.