Re: Multiple-Attribute Keys and 1NF


"JOG" <jog@xxxxxxxxxxxxx> wrote in message
news:1188498134.110552.184040@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Aug 30, 6:41 pm, "Brian Selzer" <br...@xxxxxxxxxxxxxxxxxxx> wrote:

[big snip]
Are we agreed up to there?

Not exactly. What you have are the roles Name and Language which appear
as
free variables in the predicate Speaks. A sentence in FOL is a closed
formula, for example,

exists Name exists Language Speaks(Name,Language)

Well that is certainly one possibility, and of course I realise that
it is how Codd prescribed encoding a proposition in his 1969 paper. I
am suggesting that:

Ex has_Name(x, persons_name) -> speaks_language(x, language)

is an equally valid, if not better option. Why? Because we can
explicitly incorporate attribute names (which remember Codd just
bolted on, redefining a mathematical relation in the process), and
secondly the key is clearly expressed (all attributes to the left of
the ->) - there is no need for a magic header.


I won't go here, since you've already realized that Name isn't a key. It is
true that Name multidetermines Language, however.


where each quantifier binds a free variables in Speaks. Supposing that
the
domains for Name and Language are,

Names {Jim, Brian, Sue} and
Languages {English, German, French}

respectively, an interpretation of the sentence gives,

Speaks(Jim,English) /\
Speaks(Jim,German) /\
~Speaks(Jim,French) /\
Speaks(Brian,English) /\
~Speaks(Brian,German) /\
~Speaks(Brian,French) /\
~Speaks(Sue,English) /\
~Speaks(Sue,German) /\
~Speaks(Sue,French)

Aye, but where have those all important attribute names disappeared
to?


They are encoded in the predicate Speaks. It is not important to know the
exact composition of the predicate Speaks, other than that the only free
variables that appear in it are Name and Language. The parameterized
notation above is easier to write yet conveys the same information than

(Speaks such that Name := Jim and Language := English) /\
(Speaks such that Name := Jim and Language := German) /\
....etc....


Which under the closed world assumption becomes,

Speaks(Jim,English) /\
Speaks(Jim,German) /\
Speaks(Brian,English)

From this it can be deduced that Jim speaks both English and German, and
that Jim and Brian both speak English. Under the domain closure
assumption,
it can be deduced that Sue does not exist, and that the only languages
that
exist are English and German. Sue can exist and French can exist, but
since
neither are referenced, neither does. It should be noted that just
because
Brian exists and German exists doesn't mean that Brian speaks German.
The
truth value for Speaks(Brian,German) was assigned false under the given
interpretation.

I understand this view, but all CWA (imo) should do is tell us that
no /propositions/ exist discussing sue. Surely we want a database
that, if we ask it whether sue exists, responds "not as far as I've
been told" instead of "no definitely not. no sireee. never ever"?


But that's more of an open world view, which shades the meaning of every
aspect of the database. I'm not saying it is wrong, but it should be
understood, then, that the content in the database is limited to what is
known to be true instead of what is actually true. It also provides a basis
for 3VL, since by accepting the open world interpretation, you are accepting
that there can be facts that are not known.

Also, it's not "never ever," but rather "definitely not in this picture of
reality."


If so then [P1] ^ [P2] gives us (via
composition):
Name(x, Jim) -> speaks_language(x, English) ^ speaks_language(x,
English)

and we are left with a sentence that has two distinct roles, one of
which appears twice. All of this sort of thinking has been driven by a
distaste us having to add a magic 'header' component to a relation
(probably as a consequence of reading pascal's work), and the desire
to bring roles back into the equation.

But you can
certainly assign a set of values to a variable that expects a set of
values,
since a set is a value! And you can certainly have a predicate with
free
variables that range over relations and free variables that range over
individuals--it's just that the predicate is no longer first order.




.

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