Re: a union is always a join!


"Walter Mitty" <wamitty@xxxxxxxxxxx> wrote in message
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"Brian Selzer" <brian@xxxxxxxxxxxxxxxxxxx> wrote in message
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"Walter Mitty" <wamitty@xxxxxxxxxxx> wrote in message
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"Brian Selzer" <brian@xxxxxxxxxxxxxxxxxxx> wrote in message
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that states what is happening. Whenever nothing is happening, what
has been the case /is/ the case. For example, if Joe has been second
in line

Let's look at "whenever nothing is happening" in more detail. I submit
that, at a point in time where there are no transactions in progress,
that "nothing is happening". Further, I submit that, if serializability
is the criterion for concurrency management, then the DBMS ensures that
the view of the database is as if "nothing is happening", during a
transaction, except for the actions of that transaction. Every other
transaction can be seen as being completed "in the past" or beginning
"in the future".

So, if the transactions can be serialized, each transaction sees the
database as if "nothing is happening". If you agree with all that,
then why isn't your point moot? If you don't agree, where don't you
agree?

My point has little if anything at all to do with transactions and
concurrency control. Those belong to implementations. My point is that
relational calculus, or any equivalent mechanism such as relational
algebra, while necessary for describing database updates, is not
sufficient for that purpose because it can only apply to a single
database, not two successive databases. The mechanism of updating the
database cannot be reduced to mere algebraic expressions, but instead to
asserting, in the context of what has been the case, just what in the
world is different and exactly how. Let me explain.


So, what does "whenever nothing is happening" mean in the context of the
point you are making?


In the context of the point I am making it introduces the null case: the
case where no database update is indicated because the things that have been
in the world are the things that are in the world and exactly how those
things have been related to each other is exactly how those things are
related to each other.

"What has been the case" encompasses the interval [Tn, Now), where Tn is the
instant of the last change. "What is the case" is the snapshot of the world
at the current instant. Whenever nothing is happening, "what has been the
case" will obtain at least until the succeeding instant, so nontemporal
queries against "what has been the case" must return exactly the same
results as the same queries against "what is the case." Whenever something
/is/ happening, on the other hand, at that instant "what has been the case"
becomes "what had been the case during [Tn, Tc)" where Tc is the instant of
what is happening, and since "What is the case" will obtain at least until
the succeding instant, notemporal queries against "what is the case" must
return exactly the same results as the same queries against a new instance
of "what has been the case" that encompasses the interval [Tc, Now).

A changing world can be described as a series of snapshots or as a series of
events. I prefer the latter because while the series of snapshots can be
derived from the series of events, the series of events cannot always be
derived from the series of snapshots. An expression that refers to one
individual at one time may refer to a completely different individual at
another. For example, "the person that is first in line" is definite in
that it refers to exactly one person at a time, but the statement "The
person that is first in line is wearing a red hat." could be true at
successive times even if "the person that is first in line" refers to Joe at
one time and to Mary at the next, provided both Joe and Mary are wearing red
hats. Similarly, "The person that is first in line is wearing a red hat."
could now be false because Mike, who is wearing a blue hat, is now first in
line, or because Joe just put on a blue hat. Since each event occurs in the
context of what has been the case, the confusion is eliminated because the
transition that describes the event asserts just what in the world is
different and exactly how. So it would be clear that Mike is now first in
line or that Joe just put on a blue hat.


.

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