Re: The wonderful world of keys
From: paul c <toledobythesea_at_oohay.ac>
Date: Thu, 25 Jan 2007 12:17:22 GMT
Message-ID: <md1uh.783502$1T2.365607_at_pd7urf2no>
>
>
> Small point: *every* relation has a superkey which includes all its
> attributes.
> (Put another way: for all relations R, all of R's attributes form a
> superkey.)
> You probably meant: a relation having a minimal key which includes all
> its attributes.
>
> So, I don't see anything wrong with having nothing on either the
> left or the right side of the "->". One could think of both sides
> as being in conjunctive normal form, and an empty expression
> is just the conjunction of zero terms.
>
> Consider how you would express a boolean function as
> a relation. Let's take less-than. You *could* think of it as a
> relation of three attributes:
>
> x:int, y:int -> result:boolean
>
> But it is cleaner to consider it instead as
>
> { x, y | x < y }
>
> A relation on two attributes. And what is the functional
> dependency of the above?
>
> x, y ->
>
Date: Thu, 25 Jan 2007 12:17:22 GMT
Message-ID: <md1uh.783502$1T2.365607_at_pd7urf2no>
Marshall wrote:
> On Jan 24, 8:59 am, "JOG" <j..._at_cs.nott.ac.uk> wrote:
> ...
>
>>But on considering the possibility of a relation having a superkey >>which includes all its attributes, and hence where there is no material >>implication at all in its describing predicate, I ran into a bit of a >>mental block. Perhaps my analogy is awry, I'm not certain, as I seem >>then to be saying in this case that there is nothing on the other side >>of the -> implication, other than a 'true'. Perhaps this is ok? >>Thoughts welcome.
>
>
> Small point: *every* relation has a superkey which includes all its
> attributes.
> (Put another way: for all relations R, all of R's attributes form a
> superkey.)
> You probably meant: a relation having a minimal key which includes all
> its attributes.
>
> So, I don't see anything wrong with having nothing on either the
> left or the right side of the "->". One could think of both sides
> as being in conjunctive normal form, and an empty expression
> is just the conjunction of zero terms.
>
> Consider how you would express a boolean function as
> a relation. Let's take less-than. You *could* think of it as a
> relation of three attributes:
>
> x:int, y:int -> result:boolean
>
> But it is cleaner to consider it instead as
>
> { x, y | x < y }
>
> A relation on two attributes. And what is the functional
> dependency of the above?
>
> x, y ->
>
I thought that dependency theory says (x,y) -> {}, so the right side isn't exactly nothing, rather the empty set and the dependency would be true of every true tuple when {x,y} is a superkey. And that the "implication" is true if the relation has tuples. But not always true of false tuples, ie., the complement. Darwen and co give relations with empty attribute sets a value, either true or false.
p Received on Thu Jan 25 2007 - 13:17:22 CET