Re: A different definition of MINUS, Part 3

On Dec 21, 9:14 pm, paul c <toledobythe..._at_oohay.ac> wrote:
> vadim..._at_gmail.com wrote:
>
> ...
>
> > Next one may compare D&D <AND>&<OR> based system, with RL join&inner
> > union based one in terms of consistency. Both have arguments in their
> > favor. D&D system honors distributivity, and De Morgan laws. RL honors
> > absorption, so that the subset relation can be generalized to be
> > applicable to any pair of relations. Also RL can express projection as
> > an (inner) union of a relation with an empty relation. ...
>
> In other words, D&D has absorption when projection is applied and its
> union allows deMorgan.  RL has absorption without projection but
> projection is defined in terms of a second kind of union.  They both
> have distributivity and associativity and defined identity values

Not quite. Both distributivities of ^ over v, and v over ^ are conditional. Distributivities of + over ^, and ^ over + are universal.

> although D&D needs only two identities.  

They don't need additional constants because they don't define negation. In RL negation is defined with two axioms:

x' ^ x = x ^ R00.
x' v x = x v R11.

Double negation, and De Morgan

x' + y' = (x ^ y)'

are theorems in RL.

> As for RL and deMorgan, I
> thought Marshall S said at least a year ago that RL supported deMorgan.
>   I'm not sure, does it?

x' v y' = (x ^ y)'

is not valid in RL, example

y = {<q=a,>,}
x = {<p=1,>,}

(I changed attribute names in QBQL to not collide with relation names) Received on Mon Dec 22 2008 - 07:32:52 CET