One example of cumulative aggregation would be find the total number of employees who had worked at some point for a company. To compute this value at the end of each calendar year, then, for each year, define a valid-time element which is valid from the beginning of time up to the end of that year. For each valid-time element, find all tuples which overlap that element, and finally, count the number of tuples in each set.
Instantaneous aggregation may be considered to be a degenerate case of cumulative aggregation where the partition is per chronon and the associated interval is that chronon.