Symbolizing time. The task of modeling time begins with establishing a set of symbols to refer to its various fundamental elements. The field of mathematics has done this to some extent in the use of letters to designate points and intervals of time along a scale. The thing to keep in mind with time is that its flow and segmentation is all a matter of metaphor and measurement. These two processes of conceptualization, present in most semantic fields, must be carefully separated from the objects of the real world.
The illustration in figure 1 indicates first, the fact that measurement makes time a scale involving a beginning point and a unit of length. The standard time interval indicated is the 24-hour period called a day. This is the solar cycle that has become the basis of many calendar systems. There are cycles measured by the phases of the moon and the passing of the seasons as well. We will not go into all these various ways of applying a measure to, or metrifying, time at this point in our study.
The second item on figure 1 diagrams an interval, consisting of two points along with a span of an infinite number of points lying in between them. Time is perceived as flowing from one end of the interval (t1) to the other (t2). The points in between are vaguely referred to as the path or passage (via) of time.
The third item on the figure gives an analysis of a point, which may be relatively precisely defined or to some degree quite fuzzy. The point may be more precise on one side than the other, such as when we place an event before a certain point in time. How much before is more fuzzy than its upper limit, to which it might be arbitrarily close.
Modeling time. The structure of the relationships in figure 1 can be simulated in Backus-Naur form as in figure 2.
The corresponding class diagram in the unified modeling language is given in figure 3. We have added the concept of a time period as a specific and definite interval of time.
