# Re: Relation subset operators

Date: Sun, 7 Jun 2009 04:11:29 -0700 (PDT)

Message-ID: <b24d2a5c-7f17-4e9b-bde6-01c4fc534c9e_at_o30g2000vbc.googlegroups.com>

On 7 juin, 01:09, Marshall <marshall.spi..._at_gmail.com> wrote:

> On Jun 6, 2:19 pm, vadim..._at_gmail.com wrote:

*>
**>
**>
**> > I'm still not sure if there are shorter versions. Marshall (who is
**> > apparently in stealth mode) used to work on a program that generates
**> > all valid RL expressions, and this looks like a problem fitted for
**> > such a tool. The other curiosity is how many different RL expressions
**> > one can generate with inversions and complements alone. For example,
**> > the identities
**>
**> Yes, these are both things my program can handle. The theoretical
**> aspects are fairly far along; what is killing me is the practical
**> aspects.
**> Namely, the number of possible expressions in even mildly complex
**> algebras is mega gigantic, and in algebras with operators that
**> are both commutative and associative, simply noting that two
**> complex terms of the same size are syntactically equivalent
**> is excruciatingly slow. I have recently purchased a much
**> more powerful machine but I'm not sure how much this will
**> help; the big wins have all been the results of greater
**> understanding of the nature of Universal Algebra.
*

Marshall,

For what it's worth...

For having been involved in the exercice of attempting to build a logical machine to be a sound evaluator for relational operations, I have discovered that there is an intricate relationship between the coherence of relation equation solving and the logical computing model used to actually represent a single relation, given current constraints imposed by memory/cpu architectures. In other words, the two aspects simply can hardly be dissociated: building an relation equation expressor without considering a serious work onto how there are to be represented logically (and physically as a consequence) will not only put such effort in jeopardy but will make one hit a stone dead end due to the fact that a logical expression solvers built on the principle of direct image systems relation representation, has a very limited scope of verification.

I have designed a logical and computing model based on the principle of representing relations thanks to fractal contructs which allows to exploit other effective mathematical tools than traditional ra to effectively operate relations and have the logical machine make logical inferences as to the most appropriate formulation of a relational operation. I am not sure that does make sense to somebody who's involved deeply into the logical aspect of correctness but it is a friendly word of warning.

> I still have good ideas left for how to do better, and I

*> believe a complete equational theory of Vadim's algebra
**> is mechanically achievable.
*

Yes it is but not without having a complete view of the problem and
taking into considerations the need for a sound logical representation
of relations.

*> Marshall
*

Received on Sun Jun 07 2009 - 13:11:29 CEST