Re: The wonderful world of keys
From: paul c <toledobythesea_at_oohay.ac>
Date: Thu, 25 Jan 2007 12:25:01 GMT
Message-ID: <xk1uh.798337$R63.447541_at_pd7urf1no>
>> On Jan 24, 8:59 am, "JOG" <j..._at_cs.nott.ac.uk> wrote:
>> ...
>>
>>> But on considering the possibility of a relation having a superkey
>>> which includes all its attributes, and hence where there is no material
>>> implication at all in its describing predicate, I ran into a bit of a
>>> mental block. Perhaps my analogy is awry, I'm not certain, as I seem
>>> then to be saying in this case that there is nothing on the other side
>>> of the -> implication, other than a 'true'. Perhaps this is ok?
>>> Thoughts welcome.
>>
>>
>>
>> Small point: *every* relation has a superkey which includes all its
>> attributes.
>> (Put another way: for all relations R, all of R's attributes form a
>> superkey.)
>> You probably meant: a relation having a minimal key which includes all
>> its attributes.
>>
>> So, I don't see anything wrong with having nothing on either the
>> left or the right side of the "->". One could think of both sides
>> as being in conjunctive normal form, and an empty expression
>> is just the conjunction of zero terms.
>>
>> Consider how you would express a boolean function as
>> a relation. Let's take less-than. You *could* think of it as a
>> relation of three attributes:
>>
>> x:int, y:int -> result:boolean
>>
>> But it is cleaner to consider it instead as
>>
>> { x, y | x < y }
>>
>> A relation on two attributes. And what is the functional
>> dependency of the above?
>>
>> x, y ->
>>
Date: Thu, 25 Jan 2007 12:25:01 GMT
Message-ID: <xk1uh.798337$R63.447541_at_pd7urf1no>
paul c wrote:
> 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
Correction - the "implication" is true even if the relation is empty, but not necessarily true in the complement. (I think I'd better stop now
as it is early here and this might distract me all day long.)
p Received on Thu Jan 25 2007 - 13:25:01 CET