In the last few years, a variety of contributions have come to alleviate the shortage of studies concerning the relationship between time and knowledge, though none of them uses a standard language of temporal logic. In contrast, our approach consists of formalizing a representational system based on a discrete temporal logic which boundlessly branches off both to the left and to the right. This system will allow us to refer to standard time, to define temporal distances between pairs of instants, and to express temporal properties of constant or periodic events by means of continuous or discontinuous intervals. The organization of this article is as follows. First, we will define the semantics of a temporal logic which summarizes the ontology of time from our point of view-that of Physicae Logica-as well as its operators. Subsequently, we will justify the convenience of establishing a relativistic calculus between its intervals. We will next analyze the effect of giving our logic a quantitative, rather than a qualitative orientation. Finally, we will explain the transition from a quantified Physicae Logica to a Physicae Logica with standard time. Q 1995 John Wiley & Sons, Inc.