Re: Understanding Logics with Aggregate Operators

"arthernan" <arthernan_at_hotmail.com> wrote in news:1169762817.304743.61000 _at_q2g2000cwa.googlegroups.com:

> I agree with the saying "go to the source". So I did. I do database
> programming for a living. And I want to know what else is out there,
> that is based in formal methods. I just hear that there is all this
> great research already done and we are not using it.
>
> Aggregates seem to be one missing piece in most logic description
> languages. So I decided to look up articles in the subject and I found
> this one.
>
> Logics with Aggregate Operators. (2000) (Lauri Hella).
>
> I read the first four pages just fine, but I am stuck (for now) on page
> 5. Anyway here is my problem:
>
> Notes: 1)The link to the original PDF article is at the bottom. 2) The
> symbol φ in case it's hard to read here is the Greek letter phi)
>
> I'm not sure what this formula means
>
> t(x) = y.φ(x,y) (x and y have a vector sign on top of them)

It is like the "logic with counting terms". It means t(X) = count(X) such that phi(X,Y) holds, it shows the number of elements for which Y is a place holder for each element for which X is a place holder.

>
> And then from there I think I am also missing.
>
> Aggr f y.(φ(x,y),t(x,y))
>
> I don't think I know which one is the free variable.

It is 'X'. 'Y' is bound with # (count).

>
> I think I could understand this article, but I'm not sure where to look
> or if a clarification is what I need. In any case any information is
> greately appreciated.
>
>
> http://tinyurl.com/2qe7p6
>
> or
>
> http://preview.tinyurl.com/2qe7p6
>
>
Received on Fri Jan 26 2007 - 21:33:31 CET