# Re: A different definition of MINUS, Part 3

Date: Sun, 21 Dec 2008 22:32:52 -0800 (PST)

Message-ID: <2c41b274-a4a2-4d54-b4d5-a475551f8f50_at_g39g2000pri.googlegroups.com>

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