Re: Complement in Relational Lattice
Date: Fri, 01 Jun 2007 01:58:36 GMT
Message-ID: <g3L7i.246801$aG1.76717_at_pd7urf3no>
Marshall wrote:
> On May 31, 3:36 pm, Marshall <marshall.spi..._at_gmail.com> wrote:
>
[Quoted] >>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
>
Thank you Marshall. Somewhat mixed feelings as I was hoping to spend the summer getting some old scooters on the road and now I'm obligated [Quoted] to achieve a better understanding of the RL ideas. I must admit that I didn't try very hard to understand RL ages ago, but was intrigued by its approach to union, thinking that it might be a very practical engine technique. Changing one word in the D&D Algebra definition would give the same operator, admittedly that would pervert their analogy and which was pointed out directly by others and indirectly too (I remember Jon H talking about predicates that get truncated, can't remember exactly what he said, truncated is my word, not his, still that didn't bother me). I [Quoted] am guessing that part of their resistance has to do with the very name "union" even though they suggest the name "disjoin" for the version that parallels conventional boolean algebra. Has the same result when headings "match", so I was surprised that people found it out-of-sorts with D&D, since the latter stipulate that over and over anyway!
p Received on Fri Jun 01 2007 - 03:58:36 CEST