A temporal logic, called LNint, is presented. It combines the treatment of points and intervals and declarations about dates and dated intervals like temporal logics with temporal arguments. In this way a mixture of the absolute and relative approaches to the treatment of time is obtained. LNint is a natural extension of point temporal logic over discrete time LN. It introduces expressions about events, with a syntax inspired by the logic of Halpern and Shoham, and expressions about points, that include points that belong to intervals. This will allow to express temporal relations between points, between intervals, and between points and intervals, and, in addition, to explain concepts such as the next interval, the last interval, and the inferior and superior extremes of an interval.