Re: Question about Date & Darwen <OR> operator
Date: Sun, 04 Sep 2005 00:44:44 GMT
Message-ID: <0srSe.365651$s54.327635_at_pd7tw2no>
VC wrote:
> "paul c" <toledobythesea_at_oohay.ac> wrote in message
> news:Pb6Se.67282$Hk.4881_at_pd7tw1no...
>
>>the bit on pg 56 ...
>>Hs = Hr1 union Hr2
>>Bs = {ts: exists tr1 exists tr2
>>( ( tr1 in Br1 or tr2 in Br2) and
>>ts = tr1 union tr2 }
>
>
> If the above is indeed the <OR> definition, then I do not understand how it
> handles relations with the same header..
>
> Let a tuple be a set of triples <A, T, v> (attribute, type and value).
> Further, let r1 and r2 be relations with the same header H. Now, what
> would be the result of tr1 union tr2 ? Obviously it's not a relational
> tuple any more because there are two attributes with the same name in the
> union. E.g.
>
> tr1 = { <x,int,4>, <y, char,'a'}
> tr2 = {<x,int,5>, <y, char,'b'}
>
> tr1 union tr2 = { <x,int,4>, <y, char,'a'>, <x,int,5>, <y, char,'b'> }
>
> What am I missing ?
>
>
A friend of mine who has a couple of math degrees and who I think is pretty smart in many areas, had almost exactly the same problem with the definition. My friend's example was similar to yours except that some attributes or tr1 and tr2 were disjoint. A couple of years ago, he told me that he had written to one of the authors suggesting a change but that he got no reply.
Since then, Alfredo on this group has clarified the meaning for me but not in a way that I am able to reconcile with the definition as written.
I've just assumed that's because of either my lack of mathematical training or my stupidity or more likely, both.
For all I know, you aren't missing anything. I wish the mathematicians/philosophers in the group would help me as well as you to reconcile the definition, too. The way I've been coping is to change the last bit, " and ts = tr1 union tr2" to "ts *is a member of* tr1 union tr2" but this seems a little redundant.
It occurred to me that the use of the term "ts" means a set of tuples rather than one tuple. After all, Bs is defined as a set of tuples, but this still seems to me to make that part " and ts = tr1 union tr2" redundant to my unpracticed eye, ie. if it were removed, what difference would it make? In fact, the first time I read it, I concluded, apparently wrongly, that <OR> and <AND> both produce the cartesian product when the headings are disjoint. I still wonder whether this wouldn't sometimes be a useful identity.
Not much help, I'm sure.
p Received on Sun Sep 04 2005 - 02:44:44 CEST