Re: Complement in Relational Lattice
Date: 31 May 2007 19:32:36 -0700
Message-ID: <1180652646.449634.145430_at_j4g2000prf.googlegroups.com>
On May 31, 3:36 pm, Marshall <marshall.spi..._at_gmail.com> wrote:
> RL complement is well-defined. It is roughly the complement
> of the rows and the complement of the columns.
Another way to state it.
Consider the algebra of headers that is embedded in the RL. This algebra is isomorphic to basic set algebra, with \/ as intersection and /\ as union. In this algebra, de Morgan's holds.
Consider the two valued algebra formed by considering all relations as empty or nonempty. (That is, the algebra of R \/ 00.) \/ is AND and /\ is OR. This is isomorphic to the familiar two-valued boolean algebra. In this algebra, de Morgan's holds.
The RL complement is formed with the header complement in set algebra H, the boolean complement in the row algebra B.
11 \/ H /\ B
So offhand I would expect de Morgan's to hold for RL complements.
This one's for you Paul. ;-)
Marshall Received on Fri Jun 01 2007 - 04:32:36 CEST