# Nomenclature for Aggregation of Binary Time Series Data with AND or OR

Lets say I have some hourly binary data over a couple days,

Datetime            Value
2016-01-01 00:00    1
2016-01-01 01:00    1
2016-01-01 02:00    0
2016-01-01 03:00    1
2016-01-01 04:00    0
...


I wish to aggregate this data up to a daily resolution and there are two obvious ways. The first is to treat it as intensive data and average over each day. Assuming there are only 5 reads on the first of Jan 2016 we would have

Date          Value
2016-01-01    0.6
...


The second would be by indicating if there was at least one True or at least one False reading within the time period. This could be done by using the binary OR or AND functions respectively. This would give

Date          OR    AND
2016-01-01    1     0
...


As stated in the first example this type of data is intensive - see here for more details on intensive and extensive aggregation. Is there a standard nomenclature for this second type of aggregation of data?