Re: [LIU Comp Sci] Need tutoring on Relational Calculus

On 2014-12-18, ruben safir <ruben_at_mrbrklyn.com> wrote:
> I'm pouring over the HW assignment

What are you pouring over the assignment? Syrup? No wonder you can't understand it.

Sorry about that, the word you want is "poring".

> and the explanation and notes from the text is not adequate to explain
> relational calculus.

Not unlikely. Have they really said some equivalent of "There's this other thing called Relational Calculus, so for homework read up on it here and try to apply it to the examples we've already used."? If so, are they assuming some course pre-requisite that you do not possess? If not, surely there was something about it in class first.

> The book is actually in shambles.

Probably not. It may be meant for people starting from somewhere other than where you are.

> This is a very advanced mathamtical topic and there is no way to learn
> this in a single lesson, although you might be able to bluff you way
> through it.

Yes, though I wouldn't try the "bluff" thing if I were you.

> Does anyone understand this?

Undoubtedly.

> It makes little sense as it is presented, and I'm not in any way certain
> of the meaning of the syntax.
>
> I have no idea what this whole section of 6.6.63 is out of the text.

I hope you have understood the bit before this which (presumably) explains exactly what the book means by "formula".

> Quote:
>
> In addition, two special symbols called quantifiers can appear in
> formulas; these are the universal quantifier (∀) and the existential
> quantifier (∃). Truth values for formulas with quantifiers are described
> in Rules 3 and 4 below;

So, there are these two symbols which will be explained shortly.

> *first, however, we need to define the concepts of free and bound tuple
> variables in a formula.***
> ENDQUOTE
>
> *Here is a question, Why does it matter if Tuple Variables are Free
> or Bound?****
>
> Why do we make them Free or Bound? ****

Why are you asking these questions at this point when the definition of the concepts should provide at least a first part of the answer?

> QUOTE
> Informally, a tuple variable t is bound if it is quantified, meaning
> that it appears in an (∃t) or (∀t) clause; otherwise, it is free.
> ENDQUOTE
>
> ??????

Actually I might question the book's use of "Informally" here, but I suppose it's relative, since the whole subject is very much a formal system. Or did that bit not really come before the following bits?

> QUOTE
> Formally, we define a tuple variable in a formula as free or bound
> according to the following rules:
>
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`
>
> Stop this author doesn't know the material.

Wrong.

> Either that or he doesn't know how to explain it.

An explanation has to be at an appropriate level for its audience. Maybe you are not this author's audience.

> You can't LEARN math by memorizing rules inside rule inside rule.
> You have to lay out the theory and show practical models.

That depends on the sort of maths you are dealing with. There may not be any practical models. There are pieces of pure mathematics that didn't have a practical use until 300 years after they were published.

> You have to understand why rules are used and developed

That would be nice - if there was enough time.

> and there is no effort to even attempt an explanation.

Well actually, all these things you are quoting are an attempt at an explanation.

> QUOTE
> An occurrence of a tuple variable in a formula F that is an atom is free
> in F.

Assuming you have the book's definitions of tuple variable and formula and atom, here is the heart of your earlier question. If a tuple variable is an atom, it is all by itself, and there is nothing to tell it what values it can take. It is free (note that word - "FREE") to take any value at all.

To paraphrase part of the "Formally" quote above, if a tuple variable is not free...

...it is bound!

> An occurrence of a tuple variable t is free or bound in a formula
> made up of logical connectives—(F 1 AND F2), (F1 OR F2 ), NOT(F1 ),
> and NOT(F2 )— depending on whether it is free or bound in F1 or F2
> (if it occurs in either).
>
> Notice that in a formula of the form F = (F1 AND F2) or F = (F1 OR F2),
> a tuple variable may be free in F1 and bound in F2, or vice versa; in
> this case, one occurrence of the tuple variable is bound and the other
> is free in F.

OK, if you start combining formulae to make another formula, it gets more complicated. Who's surprised?

>
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Why does it matter?

It matters because this sort of formula will end up representing a relational query, whose result is a set of actual values of a tuple variable. Before you construct the actual query (or formula) the tuple variable is free to have any value - you don't know what the answer will be. Afterwards, because of what you put in the formula, the tuple variable will be bound - to the answer you need!

> QUOTE:
>
> All free occurrences of a tuple variable t in F are bound in a formula
> F of the form F= (∃ t)(F) or F = (∀t)(F).
>
> UNQUOTE
>
> I have no idea what he is talking about here.

I assume that F^B is actually F with B as a superscript, and is just the name of another formula, indicating that tuple variables in it are bound.

> He just said above that any ∃ t or ∀t means that t is BOUND. Now it
> is free?

It is free in F. When you create F^B by adding a quantifier to F, it is bound in F^B. Simples.
>
> QUOTE
> The tuple variable is bound to the quantifier specified in F. For
> example, consider the following formulas:
> F1 : d.Dname=‘Research’
> F2 : (∃ t)(d.Dnumber=t.Dno)
> F3 : (∀d)(d.Mgr_ssn=‘333445555’)
> The tuple variable d is free in both F1 and F2, whereas it is bound to
> the (∀) quantifier in F3. Variable t is bound to the (∃) quantifier
> in F2. We can now give Rules 3 and 4 for the definition of a formula
> we started earlier:

So there's an actual example for you.

And now for the promised rules:

> Rule 3: If F is a formula, then so is (∃t)(F), where t is a tuple
> variable. The formula (∃t)(F) is TRUE if the formula F evaluates to
> TRUE for some (at least one) tuple assigned to free occurrences of t in F;
> otherwise, (∃t)(F) is FALSE.
>
> Rule 4: If F is a formula, then so is (∀t)(F), where t is a tuple
> variable. The formula (∀t)(F) is TRUE if the formula F evaluates to
> TRUE for every tuple (in the universe) assigned to free occurrences of
> t in F; otherwise, (∀t)(F) is FALSE.
>
> The (∃) quantifier is called an existential quantifier because a formula
> (∃t)(F) is TRUE if there exists some tuple that makes F TRUE.
>
> For the universal quantifier, (∀t)(F) is TRUE if every possible tuple
> that can be assigned to free occurrences of t in F is substituted for t,
> and F is TRUE for every such substitution. It is called the universal
> or for all quantifier because every tuple in the universe of tuples must
> make F TRUE to make the quantified formula TRUE.

I assume the book has more, but anyway...

> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
> So then we have this homework and I'm doing it, barerly working through
> this methodology and then you hit this:
>
> e) Retrieve the names of employees who work on every project:
>
> This question is insane with SQL and Relational Algebra (where we can
> use a division)

No, just potentially confusing, but it's the standard example for relational division.

> but solving it with relational calculus?? Who can explain an answer this?

You, when you have understood a bit more.

> This is an image of the database scheme
>
> http://www.nylxs.com/images/database_3.3_company.png

Nobody cares, unless they're going to do your homework for you instead of making a few potentially but not necessarily helpful remarks. Anyway it's a standard example schema.

Eric

-- 
ms fnd in a lbry