# Re: Relational lattice

Date: 14 Mar 2005 11:16:41 -0800

Message-ID: <1110827801.062965.41920_at_l41g2000cwc.googlegroups.com>

Jan Hidders wrote:

*> Vadim Tropashko wrote:
**> > Jan Hidders wrote:
**> >>
*

> >> The answer to your question is actually in that reference. See

*> >> Remark 7.3 on page 16. If you want to know more, the paper by
**> >> Kolaitis they refer to is actually also on-line: See Phokion's
*

home

*> >> page:
**> >
**> > OK, where is the equation?
**>
*

> It is constructed in the proof of Prop. 7.2. Each of the conditions

over

> the variable X in the list 1, .., 4 can be expressed with equations.

*>
**> > I have difficulty understanding which constructs they admit into
*

the

*> > algebra and which don't.
**>
*

> They use in the proof the standard 5 operation of the flat relational

*> algbra and furthermore you can use an arbitrary set of extra relation
**> variables (which are of course existentially quantified) next to the
**> ones in the database and the one that defines the result.
**>
**> > The concept of sparce equation also eludes me:-(
**>
**> You can ignore that for now. We only look at sets of equations over
*

flat

> relations that always define a unique result, and those are always

*> sparse anyway.
*

which works over powerset. It seems like the concept of sparse equations is merely a way of bringing powerset algebra back to earth to operate with normal ("flat") relations.

Returning back to proposition 7.2, what are the equations for conditions 3 and 4? Those conditions have universal quantifiers, which is not that much different from universal quantifier that says: "find a minimal relation that satisfies the TC recurrence relation". Received on Mon Mar 14 2005 - 20:16:41 CET