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| DATE | 2014-12-18 |
| FROM | Ruben
|
| SUBJECT | Re: [LIU Comp Sci] Need tutoring on Relational Calculus
|
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Message-ID: <5492B47E.60004-at-my.liu.edu>
Date: Thu, 18 Dec 2014 06:03:26 -0500
From: Ruben
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To: learn-at-mrbrklyn.com, learn-at-nylxs.com,
Ping-Tsai Chung ,
Ping-Tsai Chung
Subject: Re: [LIU Comp Sci] Need tutoring on Relational Calculus
References: <5492A7BC.2000001-at-panix.com>
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In predicate logic , a
*universal quantification* is a type of quantifier
, a logical
constant which is
interpreted
as "given any" or "for all". It expresses that a propositional function
can be satisfied
by every member
of a domain of
discourse . In other
terms, it is the predication
of a
property or
relation to every member
of the domain. It asserts
that a predicate
within the scope
of a
universal quantifier is true of every value
of a predicate
variable .
In mathematics , a
*predicate* is commonly understood to be a Boolean-valued function
/P/: /X/? {true,
false}, called the predicate on /X/. However, predicates have many
different uses and interpretations in mathematics and logic, and their
precise definition, meaning and use will vary from theory to theory. So,
for example, when a theory defines the concept of a relation
, then a
predicate is simply the characteristic function
or the indicator
function of a
relation. However, not all theories have relations, or are founded on
set theory , and so one must
be careful with the proper definition and semantic interpretation of a
predicate.
On 12/18/2014 05:09 AM, Ruben Safir wrote:
> 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 (?) quan-
> tifier 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 uni-
> versal 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
>
>
>
>
>
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