DTV13 — 'begins before' axiom contradicts the definition

In clause 8.2.4, in the entry for 'time interval1 begins before time interval2', the Description says the start of time interval1 is before or the same as the start of time interval2, but the Definition is narrower. The Definition also requires the end of time interval1 to be before the end of time interval2. And therefore the axiom:
Each time interval begins before the time interval.
contradicts the Definition. The same problems arise with 'time interval1 ends after time interval2'

Replace 'time interval begins before time interval' with 'occurrence occurs before time interval'

The term ‘begins before’ suggests that the axiom was unintended, but the (only) uses of the verb concept in clause 16.5 and 16.10 require that the axiom is correct. So the term is misdefined and not business-friendly. The sense of the (internal) usage of ‘t1 begins before t2’ is “t1 does not start after t2”, which uses an existing verb concept, which the definitions in clause 16 can use.
The definitions in clause 16 actually rely on a verb concept ‘occurrence begins before time interval’ that does not exist, while ‘occurrence starts before time interval’ does. So, the simple solution is to rephrase the uses and delete this verb concept altogether. And the same reasoning applies to ‘ends after’.
The cited definitions in clause 16.5 also use ‘occurrence occurs before time interval’ and ‘occurrence occurs after time interval’, which are not declared, either. Those concepts have obvious business usage, and are added.
The uses of ‘begins before’ and ‘ends after’ in 16.10 are addressed by Issue DTV13-87.