A New Kind of the Generalized R-implication on Interval-set

The research implication is the emphasis and difficulty in the study of logic. In the paper, the operations are redefined on the interval-set, which are interval-intersection, interval-union, interval-complement and interval-implication. Regularities and monotonicities of interval-implication are proved; interval-intersection and interval-implication are proved to be an adjoint pair; interval-implication is proved to be a generalized R-implication. Moreover, 〈I(2^U), |∩̅|, ⇒〉 is proved to be complete residuated lattice, and its properties are examined.