What I think is less clear is what that means for temporal primary keys. As Paul pointed out upthread, in every other case, a temporal primary key is at least as unique as a regular primary key, but in this case, it isn't. And someone might reasonably think that a temporal primary key should exclude empty ranges just as all primary keys exclude nulls. Or they might think the opposite.
Fascinating. I think you're absolutely right that it's clear that two empty intervals don't conflict. If somebody wants to claim two intervals conflict, they need to point to at least one instant in time that is common between them.
But a major point of a primary key, it seems to me, is that it uniquely identifies a row. If items are identified by a time range, non-overlapping or not, then the empty range can only identify one item (per value of whatever other columns are in the primary key). I think for a unique key the non-overlapping restriction has to be considered an additional restriction on top of the usual uniqueness restriction.
I suspect in many applications there will be a non-empty constraint; for example, it seems quite reasonable to me for a meeting booking system to forbid empty meetings. But when they are allowed they should behave in the mathematically appropriate way.
