Re: Interpretation of Relations

On 2007-01-19 21:22:02 +1000, paul c <toledobythesea_at_oohay.ac> said:

> Joe Thurbon wrote:

...

>>
>> Relation R_People = <<D_People>: {{Joe}}>
>> Relation R_Hair Colour = <<D_People X D_Hair>: {{Joe, Blond}}>
>>
>> (The bit in the <> is the relation header, the subsequent sets are the
>> relation body).

...

>>
>>
>> R_Hair Colour: <<D_People X D_Hair>: {}>
>>
>> indicates that I don't know the colour of Joe's hair. It really means
>>
>> NOT Joes hair is Red
>> NOT Joes hair is Blond
>>
>> Is this right? ...

...

> 
> I think this is something that often trips me up - we can obtain tuples 
> that have no attributes only by projecting away other attributes (which 
> I believe is the purpose of TABLE_DEE and DUM)

Sorry, you've lost me there.

> or by declaring a relation that has no attributes and then "assigning" 
> (basically, this means memorizing) a value that stands for true or 
> false to that relation.

Can you do this? I thought that 'attributes' were effectively names of domains, so if there are no attributes, there are no domains from which you can "assign". What would it look like?

>  In the RM, it is a logical mistake to assign an imagined value of 
> "empty set" to a tuple that has non-set-valued attributes, eg., as in 
> "R_Hair Colour: <<D_People X D_Hair>: {}>".

I think that my notation was a little confusing, in particular, notice in the first two relation above, there are double curley braces.

So

Relation R_People = <<D_People>: {{Joe}}>

means the body has one tuple, the tuple {Joe}

whereas

R_Hair Colour: <<D_People X D_Hair>: {}>

has a body with no tuples. For completeness, another possible R_Hair Colour might be

R_Hair Colour: <<D_People X D_Hair>: {{Joe, Blond}, {Joe, Red}}>

wherein the body has two (and in this case all possible) tuples defined in it.

Of course, I'd be kidding myself. I'm closer to glabrous.

Cheers,
Joe Received on Sat Jan 20 2007 - 03:50:03 CET