To compute the aggregate, first partition the time-line into valid-time elements, then associate an interval with each valid-time element, assemble the tuples valid over each interval, and finally compute the aggregate over each of these sets. The value at any instant is the value computed over the partitioning element that contains that instant.
The reason for the associated interval with each temporal element is that we wish to perform a partition of the valid time-line, and not exclude certain queries. If we exclude computing the aggregate on overlapping intervals, we exclude queries such as ``Find the average salary paid for one year before each hire.'' Such queries would be excluded because the one-year intervals before each hire might overlap.
Partitioning the time-line is a useful capability for aggregates in temporal databases (+R1,+R3).
One example of valid-time partitioning is to divide the time-line into years, based on the Gregorian calendar. Then for each year, compute the count of the tuples which overlap that year.
There is no existing term for this concept. There is no partitioning attribute in valid-time partitioning, since the partitioning does not depend on attribute values, but instead on valid-times.
Valid-time partitioning may occur before or after value partitioning.