Re: What to call this operator?
Date: Wed, 29 Jun 2005 10:11:09 +0200
Message-ID: <MPG.1d2c7604546f822b9896bd_at_news.ntnu.no>
In article <1119976637.137573.61210_at_g47g2000cwa.googlegroups.com>,
mikharakiri_nospaum_at_yahoo.com says...
> I wonder how far this algebra is developed. Both binary operations
> <AND> and <OR> are idempotent, commutative and accociative. This three
> properties are enough to define a semilattice. That is we have 2
> semilattices:
> 1. the upper semilattice for <OR>
> 2. the lowe semilattice for <AND>
> Each semilattice defines a partial order relation, one for upper
> lattice
> x<=y iff y=x<OR>y
> and one for lower one
> x<=y iff x=x<AND>y
> Even though I slopily used the same symbol "<=", these two partial
> orders are incompatible unless the algebra meet the *Absorption Law*.
> Absorption law merges the two semilattices into a single lattice.
This is very interesting. Would you mind elaborating? Can you formalise the absorption law? How did you arrive at these partial order definitions?
> Unfortunately, D&D algebra doesn't meet the absorption law. The Lattice
> algebra that I mentioned in the other thread does. The partial order
> there is a generalization of the "is subset of" relation applied to the
> any pair of database relations, even those with different headings.
> Neither of those algebras (D&D,nor Lattice) is boolean. D&D has nice
> distributivity property, although without absorption it doesn't buy us
> much.
Why is this absorption so important?
-- JonReceived on Wed Jun 29 2005 - 10:11:09 CEST