Re: Expressions versus the value they represent

On Apr 15, 5:01 am, com..._at_hotmail.com wrote:
> On Apr 12, 1:13 am, David BL <davi..._at_iinet.net.au> wrote:
>
> > If
> > this is how the RM is meant to fit into the picture
>
> You have a lot of confusions and misunderstandings about
> FOPL, relations, RVAs, Prolog and programming abstraction.
>
> If you would properly write out the simplest database
> some of this would begin to become apparent to you.
>
> What are the names of your relation variables and constants?
> What is the characteristic predicate
> (parameterized statement about the world) for each?
> What is the formal wff for each? Why?
> What are the attributes for each? Why?
> What is your (example) query relation expression?
> What is the characteristic predicate of its result? Why?
> What are the (example) values of your relation variables?
> What statement does each make about the world? Why?
> What statement does the database make about the world? Why?
> What is the value of your query relation expression? Why?
> What statement does this value make about the world
> in the context of this query relation expression? Why?
> What statement does a query result make about the world
> regardless of its query relation expression? Why?
>
> The most important things to understand are that:
> 1. each relation expression corresponds to a certain wff and
> 2. equivalent relation expressions correspond to equivalent wffs
> The relational algebra is just another syntax for FOPL.
> (So they can't possibly be at odds.)

You are merely talking about the correspondence between formulae in FOL versus expressions in the RA. E.g.

RA: project((R1 join R2) union R3, {X}) FOL: exists y,z such that (P1(x,y) /\ P2(y,z)) \/ P3(x,y,z)

R1,R2,R3 are relvar names. X is an attribute name. P1,P2,P3 are predicate symbols. x,y,z are variables.

My original post concerned *terms* in FOL which are not formulae. If you disagree with something I said then why don't you discuss that rather than something unrelated?

> The meaning of an RVA or a TVA, as with any attribute,
> is whatever the predicate of its containing relation gives it.
> Any attribute value could denote an abstract value or just itself.

In a formal semantic on a FOL there is a given "domain of discourse" which is the set (of "values") over which quantification is deemed to take place. Each FOL term represents a "value" which is a single element of this set. The interpretation of an n-ary predicate symbol is the indicator function of some given set of n-tuples of elements of the domain of discourse.

A formal semantic says nothing about the "meaning" of the counterpart to an attribute (which in FOL corresponds to a variable on which a predicate is parameterised). I challenge you to formalise what you said above. What is a formal definition of the "meaning" of an attribute? What exactly does it mean for an attribute value to "denote" something? To be frank you don't appear to know what you're talking about.

It appears you might claim for example that a predicate parameterised by a circle value "really means" a predicate parameterised by a square value (say of the same area as the circle), thereby concluding that the circle in fact "denotes" a square. That's just silly.

[snip] Received on Thu Apr 15 2010 - 03:34:03 CEST