temporal data constraints

Let's say I have two relvars like:

RELVAR R { A INTEGER, B INTEGER } KEY { A }
RELVAR S { A INTEGER, C INTEGER } KEY { A }
CONSTRAINT ( JOIN { R, S } { A } = S { A } )

That is, every tuple in S has a corresponding tuple in R but the
reverse is not necessarily true. In SQL, one might represent this by a
single SQL table with (A, B, C) such that C is NULLable (I'm not
suggesting that one should do this).

Now, I'd like to make the relation temporal, in the way that CJ Date
suggests in "Temporal Data and the Relational Model".

It's already in 6NF. I can create "since" and "during" relations like:

RELVAR R_SINCE { SINCE TIMESTAMP, A INTEGER, B INTEGER } KEY { A }
RELVAR R_DURING { DURING INTERVAL, A INTEGER, B INTEGER } KEY { A,
DURING }
RELVAR S_SINCE { SINCE TIMESTAMP, A INTEGER, C INTEGER } KEY { A }
RELVAR S_DURING { DURING INTERVAL, A INTEGER, C INTEGER } KEY { A,
DURING }

That seems like a great solution, but the problem is constraints.
Every A must have a corresponding B at all times that A itself exists,
but A may or may not have a C at any given time. I'd like some simple
constraints to illustrate that in a temporal database the same way I
represented it in the non-temporal database.

More specifically:
(1) The "during" intervals for a given A in R_DURING must form a
continuous, non-overlapping interval ending at the "since" timestamp
for that A in R_SINCE.
(2) The "during" intervals for a given A in S_DURING must be non-
overlapping, and the latest ending time of the interval must be less
than or equal to the "since" timestamp for that A in S_SINCE, if it
exists.

These two constraints, if I'm correct, ensure that no "snapshot" in
history (or the present) that recreates R and S ever violates the
constraints of those relations.

First of all, am I correct that those two constraints satisfy the
requirements?

Second, what's an effective way to represent these constraints in a
readable way? Everything I come up with involves using some kind of
MAX aggregate, but I don't know what the maximum interval ending time
is in the case that R_DURING or S_DURING is empty.

Also, how does one effectively query historical data when the key (in
this case A) changes over time?

This is an open-ended question, any guidance is appreciated.

.

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