Re: TRUE and FALSE values in the relational lattice

From: Vadim Tropashko <vadimtro_invalid_at_yahoo.com>
Date: Tue, 19 Jun 2007 14:06:18 -0700
Message-ID: <1182287178.177889.165610@d30g2000prg.googlegroups.com>

On Jun 19, 1:32 pm, Marshall <marshall.spi..._at_gmail.com> wrote:
> Not to be contrary, but I've revised my thinking in that area.
> I now equate 10 as false rather than 00. Any other relation
> equates to true, especially, of course, 01.

Propositional logic is a predicate calculus of zilliary predicates (zilliary predicates are the ones that have less arguments than unary ones:-) Therefore, associating any other relation than 01 and 00 with TRUE and FALSE, correspondingly, doesn't seem right.

> The relevance that 00 plays is in relation to existential
> quantification.
> I interpret existential quantification as meaning a relation is not
> empty.

Could you please be more specific?

Assuming the domain x = {a,b,c,d,...} the relation "exists(x) R(x,y)" evaluates to

R(a,y) \/ R(b,y) \/ R(c,y) \/ R(d,y) \/ ...

I don't see any emptiness here.

> We can define exists(X) as:
>
> X | 00 = 01

You lost me here as well. Perhaps, you mean that the relational equality is an operator that evaluates to a certain relation? Can you be more specific? Received on Tue Jun 19 2007 - 16:06:18 CDT