Re: Multiple-Attribute Keys and 1NF

On Aug 30, 6:41 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> "JOG" <j..._at_cs.nott.ac.uk> wrote in message
>
> news:1188473234.300000.41360_at_w3g2000hsg.googlegroups.com...
>
>
>
> > On Aug 30, 1:41 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> >> "JOG" <j..._at_cs.nott.ac.uk> wrote in message
>
> >>news:1188422471.161668.86550_at_r29g2000hsg.googlegroups.com...
>
> >> > On Aug 29, 7:03 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> >> >> "JOG" <j..._at_cs.nott.ac.uk> wrote in message
>
> >> >>news:1188393382.112445.286350_at_19g2000hsx.googlegroups.com...
>
> >> >> > On Aug 29, 12:49 pm, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> >> >> >> JOG wrote:
> >> >> >> > On Aug 29, 6:10 am, "David Cressey" <cresse..._at_verizon.net>
> >> >> >> > wrote:
>
> >> >> >> >>"JOG" <j..._at_cs.nott.ac.uk> wrote in message
>
> >> >> >> >>news:1188327226.729673.127810_at_r34g2000hsd.googlegroups.com...
>
> >> >> >> >>>Okay, sure. But then to be able to query for green and yellow
> >> >> >> >>>individually one must employ a further relation encoding two
> >> >> >> >>>more
> >> >> >> >>>propositions that state "'Green and yellow' contains 'Green'"
> >> >> >> >>>and
> >> >> >> >>>that
> >> >> >> >>>"'Green and yellow' contains 'Yellow'" respectively. One then
> >> >> >> >>>has a
> >> >> >> >>>schema with two domains - one for the composites and one for
> >> >> >> >>>individual colours (which is what I was inferring when I
> >> >> >> >>>initially
> >> >> >> >>>said a new one was being added).
>
> >> >> >> >>It took me a while to realize that what you meant from your
> >> >> >> >>original
> >> >> >> >>description was that
> >> >> >> >>"a green and yellow wire means earth". I had thought you meant
> >> >> >> >>"a
> >> >> >> >>green
> >> >> >> >>wire means earth" and "a yellow wire means earth". Pardon me
> >> >> >> >>for
> >> >> >> >>being
> >> >> >> >>dense.
>
> >> >> >> >>Clearly what we have here is not a domain of colors, but a
> >> >> >> >>domain
> >> >> >> >>of
> >> >> >> >>color
> >> >> >> >>codes, where a color code contains one or more colors, and
> >> >> >> >>maybe a
> >> >> >> >>"thick
> >> >> >> >>or thin" qualifier on each color.
>
> >> >> >> >>It's not clear to me why you need to able to query on simple
> >> >> >> >>colors,
> >> >> >> >>unless
> >> >> >> >>you need to decompose the color coding scheme into its
> >> >> >> >>constituent
> >> >> >> >>parts for
> >> >> >> >>some reason.
>
> >> >> >> >>There are lot of code domains where each code is made up of a set
> >> >> >> >>of
> >> >> >> >>more
> >> >> >> >>primitive elements.
> >> >> >> >>Perhaps a very relevant one might be "character code". If I have
> >> >> >> >>the
> >> >> >> >>following primitive elements:
>
> >> >> >> >>B1, B2, B4, B8, B16, B32, B64, B128
> >> >> >> >>(which might be an odd way of labelling bits 0 through 7 of a
> >> >> >> >>byte),
> >> >> >> >>I
> >> >> >> >>can
> >> >> >> >>think of the character code for 'A' as being B64+B1. Now I could
> >> >> >> >>query
> >> >> >> >>on
> >> >> >> >>all the character codes without necessarily having an operator
> >> >> >> >>that
> >> >> >> >>would
> >> >> >> >>yield "all the codes that include B1".
>
> >> >> >> >>I think that the colors, as constituents of color codes, play
> >> >> >> >>the
> >> >> >> >>same
> >> >> >> >>role
> >> >> >> >>as bits, as constituents of character codes. Do you agree?
>
> >> >> >> > Yes. I mean no. No, yes. Gnngh ;)
>
> >> >> >> > Ok, of course I understand your point - a wire can be viewed as
> >> >> >> > having
> >> >> >> > a colour code, which itself has constituent parts. But its just
> >> >> >> > one
> >> >> >> > interpretation right. I am still seeing a difference between the
> >> >> >> > propositions:
> >> >> >> > * There is a colour-code "yellow and green" that denotes "earth".
> >> >> >> > * The casing of an earth wire features the colour yellow and the
> >> >> >> > colour green.
>
> >> >> >> > Its just like the difference between the propositions:
> >> >> >> > * My office is B42
> >> >> >> > * My office is on floor B, room 42.
>
> >> >> >> > There are instances where I may well want to encode as the second
> >> >> >> > proposition forms. And /if/ that were the case (iff), well 1NF is
> >> >> >> > precluding me from doing this in terms of the wire example.
>
> >> >> >> I disagree. You have already noted that 1NF allows this with
> >> >> >> exactly 2
> >> >> >> relations (or with 1 relation and one or more operations on the
> >> >> >> color
> >> >> >> code domain.)
>
> >> >> > True, I do see that, but it does so by requiring the invention of a
> >> >> > colour-code concept which isn't in the proposition "The casing of an
> >> >> > earth wire features the colour yellow and the colour green".
>
> >> >> You have to consider the entire relation value: what about the
> >> >> propositions
> >> >> (treating or exclusively, of course):
>
> >> >> "The casing of a live wire features the colour brown or the colour
> >> >> red."
>
> >> >> "The casing of a neutral wire features the colour blue or the colour
> >> >> black."
>
> >> >> Write a predicate for the relation schema that when extentially
> >> >> quantified
> >> >> and extended yields a set of atomic formulae that implies all three of
> >> >> the
> >> >> propositions above. I think you'll find that the colour-code concept
> >> >> is
> >> >> in
> >> >> that predicate.
>
> >> > I agree. I hold little stock with set based values so in RM I would go
> >> > for the addition of colour-code foreign key.
>
> >> > But what if we weren't tied to a traditional relational schema and
> >> > tweaked the system so it could allow propositions with more than one
> >> > role of the same name without decomposing them. As Jan pointed out
> >> > 'tuples' are no longer functions - they would be unrestricted binary
> >> > relations (subsets of attribute x values). We could produce a
> >> > comparatively simpler and less cluttered schema, predicate in a very
> >> > similar manner as before, and with a few simple alterations could have
> >> > an equally effective WHERE mechanism. My concern however would be the
> >> > consequences to JOIN.
>
> >> I'm not sure I understand what you are driving at. In the example you
> >> provided, it is the combinations of values from a simple domain that have
> >> significance, regardless of whether they're wrapped in a single attribute
> >> or
> >> not. To me it doesn't make sense to have multiple attributes with the
> >> same
> >> name--the attribute names correspond to free variables in a predicate:
> >> how
> >> could you assign multiple values to the same variable?
>
> > Well consider it this way. If I have the propositions:
>
> > The person named Jim speaks the language English
> > The person named Jim speaks the language German
> > The person named Brian speaks the language English
>
> > I have three propositions, and hopefully we'd agree there are two
> > roles in these propositions: name and speaks_language. So in FOL I
> > could write these propositions as:
> > [P1] Name(x, Jim) -> speaks_language(x, English)
> > [P2] Name(x, Jim) -> speaks_language(x, English)
> > [P3] Name(x, Brian) -> speaks_language(x, English)
>
> > 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.

>
> 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?

>
> 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"?

>
> > 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.
Received on Thu Aug 30 2007 - 20:22:14 CEST