[LIU Comp Sci] Need tutoring on Relational Calculus

From: ruben safir <ruben_at_mrbrklyn.com>
Date: Thu, 18 Dec 2014 05:11:34 -0500
Message-ID: <m6u986$qe8$1_at_reader1.panix.com>

I'm pouring over the HW assignment and the explanation and notes from the text is not adequate to explain relational calculus. The book is actually in shambles. 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.

Does anyone understand this? 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.

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;

*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? ****

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 ??????

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. Either that or he doesn't know how to explain it. You can't LEARN math by memorizing rules inside rule inside rule. You have to lay out the theory and show practical models. You have to understand why rules are used and developed and there is no effort to even attempt an explanation.

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

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.

---

Why does it matter?

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

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:
■
■
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.

---

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

This is an image of the database scheme

http://www.nylxs.com/images/database_3.3_company.png Received on Thu Dec 18 2014 - 11:11:34 CET