Understanding Logics with Aggregate Operators

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)

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.

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 Thu Jan 25 2007 - 16:06:57 CST