Re: Proof of Completeness of Algebraic Properties of Relational Lattice

From: Marshall <marshall.spight_at_gmail.com>
Date: 29 May 2006 20:33:13 -0700
Message-ID: <1148959993.223814.306690@j33g2000cwa.googlegroups.com>

Mikito Harakiri wrote:
> Vadim Tropashko wrote:
> >
> > A /\ (B \/ C) >= (A /\ B) \/ (A /\ C)
>
> This identity is true in any lattice, not only relational one. Hence it
> can be proved witut need to invoke distributivity criteria.

Upon further investigation, it appears impossible to create a form of the distributive equation such that the distributor appears on the right/undistributed side. If that is in fact the case, then it appears further impossible to transform any equation into either conjunctive or disjunctive normal form. Which pretty much cuts off the entire line of reasoning I was using.

Jan has stated that semantic equivalence is undecidable in the RA. I strongly suspect that there is a simple procedure to transform the classical RA into the RL, in which case we would expect that this would also be undecidable for the RL.

(All the above is merely informed conjecture.)

At this point I see no further reason to pursue this line of inquiry.

Marshall Received on Mon May 29 2006 - 22:33:13 CDT