Re: Question about Date & Darwen <OR> operator
Date: 6 Sep 2005 05:28:07 -0700
Message-ID: <1126009687.683586.303010_at_g44g2000cwa.googlegroups.com>
Mikito Harakiri wrote:
> VC wrote:
> > "Mikito Harakiri" <mikharakiri_nospaum_at_yahoo.com> wrote in message
> > news:1125711068.995070.322110_at_g44g2000cwa.googlegroups.com...
> > [...]
> > > Well, the formal definition of <OR> and <AND> seems to be very
> > > consistent with boolean logic. Take
> > >
> > > Relation A
> > > x y
> > > - -
> > > 1 a
> > > 2 b
> > >
> > > and
> > >
> > > Relation B
> > > y z
> > > - -
> > > a #
> > > b %
> > >
> > > Then, formally relation A is a proposition
> > >
> > > x=1 & y=a \/ x=2 & y=b
> > >
> > > while relation B is
> > >
> > > y=a & z=# \/ y=b & z=%
> > >
> > > The <OR> is just formal disjunction
> > >
> > > x=1 & y=a \/ x=2 & y=b \/ y=a & z=# \/ y=b & z=%
> > >
> > > that could be equivalently transformed into
> > >
> > > x=1 & y=a & z=# \/
> > > x=1 & y=a & z=% \/
> > > x=2 & y=b & z=# \/
> > > x=2 & y=b & z=% \/
> > > x=1 & y=a & z=# \/
> > > x=2 & y=a & z=# \/
> > > x=1 & y=b & z=% \/
> > > x=2 & y=b & z=%
> > >
> >
> > The above transformation ain't correct. In fact such transformation cannot
> > be performed because x,y and z's domains are not specified.
>
> Well, it's not that hard to fix it, right? If domain z is {#,$,%} then
> the first conjunct
>
> x=1 & y=a
>
> expands into
>> x=1 & y=a & z=$ \/
> x=1 & y=a & z=# \/
> x=1 & y=a & z=% \/
Sure, it's not hard but it's not obvious from your example. Besides, you employ a strange language there:
"Then, formally relation A is a proposition"
A relation is not a proposition. A relation is a set. Neither is "x=1 & y=a \/ x=2 & y=b" a proposition, it's a predicate.
More importantly, you do not transform the predicate "x=1 & y=a" into
"
x=1 & y=a & z=# \/ x=1 & y=a & z=$ \/ x=1 & y=a & z=% \/
"
according to the rues of formal logic, you interpret it, narrowly, according to your need in your chosen domain of interpretation.
Other than that, the interpetation is OK ;)
>
> etc.
Received on Tue Sep 06 2005 - 14:28:07 CEST