An algebraic approach to granularity in time representation

Any phenomenon can be seen under a more or less precise granularity, depending on the kind of details which are perceivable. This can be applied to time. A characteristic of abstract spaces such as the one used for representing time is their granularity independence, i.e. the fact that they have the same structure at different granularities. So, time “places” and their relationship can be seen under different granularities and they still behave like time places and relationship under each granularity. However, they do not remain exactly the same time places and relationship. Here is presented a pair of operators for converting (upward and downward) qualitative time relationship from one granularity to another. These operators are the only ones to satisfy a set of six constraints which characterize granularity changes.