Interval logic and its extension

In general, interval logic has an interval truth value [n, p], where n and p are numerical truth values of [0, 1] and a condition n⩽p has to be satisfied. The author extends interval logic such that the condition n⩽p is removed from the interval truth value, that is, the interval logic has a truth value [a,b]. where a and b are any elements of [0, 1]. In this extended interval logic, degrees of ambiguity and contradiction as well as degrees of true and false can be treated. By introducing two partially ordered relations on the set of truth values of interval logic, concerning truth and ambiguity, basic logic operations are defined. Some fundamental properties of an interval logic function are studied, where an interval logic function is a function represented by a logic formula consisting of these operations and variables which take interval truth values