DTV11 — DTV Issue: Relationship among time points, time scales, and time indices

In DTV clause 8.5, the second Necessity of 'time scale has time point' reads 'Each time point is of exactly one time scale.' This is clearly wrong. Several of the time points defined in clause 10.2 are on multiple time scales. For example, 'time of day' is defined as a 'time point that is on a time scale that has a granularity that is less than 1 day'. Examples include 'second of day' and 'second of hour'.

Also in clause 8.5, the verb concept 'time point has index' makes no sense. A time point has different indices, depending upon what scale is used. This should be a ternary verb concept: 'time point has index on time scale'.

Numerous Definitions and Necessities depend upon a verb concept 'time point is on time scale' that is not defined anywhere but could be a Synonymous Form of 'time scale has time point'. Examples include:

• clause 10.2, definition of 'time of day' (see above)
• clause 11.2, most definitions
• clause 13.2, most definitions

There are no time points in 10.2 (or any other clause) that are on multiple time scales. ‘time of day’ is not a time point; it is a ‘time point kind’ – a general category of time points. Each ‘second of day’ time point is only on the day of seconds time scale, and each ‘second of hour’ is only on the ‘hour of seconds time scale’. The referenced Necessity in 8.5 is valid, and is important. As a consequence of it, the concept ‘index of time point’ is well-defined.
The form ‘time point is on time scale’ is used as described, and it should be a synonymous form for ‘time scale has time point’.