A new kind of flexible interval-implication

The implication is the emphasis and difficulty in the study of logics. From the point of view of interval structure, the operations of the universal logics including interval-intersection, interval-union, interval-complement and interval-implication are redefined based on the radical models. Regularity and monotonicity of interval-implication are proved; interval-intersection and interval-implication are proved to be an adjoint pair. In the paper, operation models of the interval-implication are firstly given in the special points of h. It is very important to the further study on flexibility of the interval-logics.