I can't remember where in his papers Codd stated the Information
Principle but here's a version of a quote by Date: "The entire
information content of a relational database is represented in one and
only one way: namely, as attribute values within tuples within relations."

Recently there has been mention of logical connectors being implicit in
tuples, eg. Mr. Scott wrote: "Each row of the join represents a
conjunction of propositions, one for each operand", ie., what I think is
called a compound proposition. I sometimes write similar, as well
regarding disjunctions. But usually my purpose is simply to understand
the algebra.

I would like to ask where is the "information" to the effect that
certain rows represent compound propositions recorded?

"paul c" <toledobythesea (AT) oohay (DOT) ac> wrote

Where is the "information" to the effect that 2 + 2 = 4 recorded? Certainly
not as attribute values within tuples within relations.

Mr. Scott wrote:
The values to satisfy that equation might well be recorded in relational
form but I presume you are not referring to that, rather to the general
truth of the equation as far as conventional arithmetic interpretation
is concerned.

I usually try to stay out of the discussions here about truth because a
database mechanism is not capable of appreciating that concept the way
humans can, just as a database doesn't record persons, only the symbols
we use for their names. No offense intended, but I think the question
borders on mysticism, imputing human concepts to a db, what Bob B uses
the anthrop-word to describe. We are all susceptible to those two
attitudes but I think we should make an effort to fall prey to them.

paul c wrote:
Oops, meant to say "make an effort to not fall prey to them".

"paul c" <toledobythesea (AT) oohay (DOT) ac> wrote

Let's explore a simple example. Suppose that a database embodies the
following sentence,

forall x forall y forall z Pxy \/ Qxz

The database has two tables, let's call them P and Q, with predicates Pxy
and Qxz respectively.

Now suppose that at a given moment,

P has rows {{x:a,y:b},{x:a,y:c},{x:b,y:c}}
Q has rows {{x:a,z:d},{x:c,z:d}}

then P JOIN Q would have rows {{x:a,y:b,z:d},{x:a,y:c,z:d}}

Now let's apply logic.

The ground formulas represented in P are Pab, Pac, Pbc.
The ground formulas represented in Q are Qad, Qcd.

What is represented in P JOIN Q? Pab /\ Qad, Pac /\ Qad.
That's because P JOIN Q has the complex predicate Pxy /\ Qxz..
x being free in both P and Q is important because only those ground formulas
in P and Q that have a common x value satisfy the predicate of P JOIN Q.

It should be clear now that it is the nature of join that dictates that
certain rows represent compound propositions, but there is more. The
dependencies defined on the database also have an impact. There really
isn't space here to go into detail, but suppose that the database embodies
the sentence,

forall x forall y forall z Pxy -> Qxz

Now the database still consists not only of the same two tables, but also an
inclusion dependency from P[x] to Q[x].

forall x forall y forall z Pxy iff Qxz

Here the database would consist of just one table but each row would
represent a biconditional.

Mr. Scott wrote:
....
I have no argument about the application of logic. Perhaps my point has
more to do with the language devices, such as 'insert', that are
essentially an assignment. While they are defined in logical terms they
are outside logic in the sense that when they are applied, something
special happens, a 'die is cast', as it were.

(Once we enter the realm of assignment, talk of possible base and view
differences is inevitable. I don't think it's inapt to say that
treating views differently from base values amounts to saying that
assignment is polymorphic, ie., behaves differently depending. I don't
see a necessary reason for that. But when dealing with a value that is
the result of assignment, I think it remains clear that the view
definition is effectively no more than a constraint on the view's value,
and not a constrain on the base values in the expression of the view's
definition. This may seem fuzzy and mystical perhaps due to my language
not being really up to the task but if that can be forgiven, I would say
that it is better to subtract notions than add them, ie., better to not
introduce a difference.)

paul c wrote:
Maybe it's useful to ask this: Was Codd trying to introduce assignment
to logic, (eg. was he trying to augment predicate calculus) or was he
trying to apply logic to the assignment of recorded values?

Snipped
Can you ellaborate on what you mean by *assignment*. If we are to
consider assignment in the sense of value assignment to a variable
then assignement is a simply component of mathematical logic.
Therefore, I do not see to define one according to the other through
precedence but rather through inclusion.

IMHO...

Cimode wrote:
Yes, I mean assignment to a (programming) variable. I don't know of any
logical operator called 'assignment'.

On 30 oct, 19:41, paul c <toledobythe... (AT) oohay (DOT) ac> wrote:
tends to restrict the possible meaning of assignment to a logical
assignment only to logical constructs such as relation variables.

Coming back to your question, though I could have hard time
understanding how pure logic could be applied to a programming
assignment, (which on an elementary sense is nothing but the semantic
representation of a physical memory bit manipulation) whithout a
relevant storage mechanism computing model defined first, I could
imagine it as being a possible assumption of his for the future
development of RM. My guess is he had enough to deal with on the
logical side of things.

On the other hand, I strongly doubt you first other assumption. But I
may just be wrong about that.