Re: Undefinedness

On 24 nov, 02:03, JOG <j..._at_cs.nott.ac.uk> wrote:
> On Nov 23, 9:44 pm, Cimode <cim..._at_hotmail.com> wrote:
>
>
>
> > On 21 nov, 14:34, JOG <j..._at_cs.nott.ac.uk> wrote:
>
> > > Word up CDT. How the devil are you all? Well, I return with a question
> > > that as ever highlights my complete lack of formal mathematical
> > > training, and in light of knowing no logicians in my daily life (funny
> > > that), I was hoping that one of you kind folks might be able to
> > > advise:
>
> > > Say I had a set of 3 encoded propositions:
> > > R := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)}, {(Name,
> > > Harry)} }
>
> > > (note that Harry's Age is missing, so instead of adding a null, i've
> > > intentionally just left the attribute out. Just ride with such oddness
> > > for now if you would.)
>
> > > What if I deigned to create a simple 'adults' subset of this set of
> > > propositions, by creating a predicate that only returned the elements,
> > > p, which contained an age attribute greater than 18. Could I state
> > > this as (where E signifies set membership):
>
> > > Adults := { p E R | EXISTSx ( x > 18 && (Age, x) E p ) }
>
> > > My question obviously hinges around Harry's missing age attribute. In
> > > this case would the EXISTSx (...) part of the set's intension simply
> > > return a FALSE, or will I end up in the quagmire of 3VL with an
> > > UNDEFINED? My instinct is that I am still in 2VL given there is no
> > > null floating about, but since the recent, excellent discussions of
> > > Jan's DEF operator, and having delved into beeson's logic of partial
> > > terms, I am not at all confident.
>
> > > Any comments are much appreciated, and regards to all, Jim.
>
> > I do not understand how you can already go to any form of subtyping
> > without a valid proposition allowing to establish relation R?
>
> Well first, I'm not sure that I'd refer to specifying a subset of
> propositions as 'subtyping'
It's true that when one assumes that a set of valid propositions ought to respect a close world assumption, one tends to attempt to seek a matching relation. I apologize for this relational bias. Given the fact that I do have this bias I obviously tend to perceive Adults as a subtype of decomposed relation RAges.

>, second, all the propositions are valid as
> far as I can tell (their pretty simple ones after all),
Depends what you imply by *valid*...
In the relational perspective, the fact that they respond to binary logic is a necessary but not sufficient criteria to consider them as valid.
> and third, R
> isn't a relation. Regards, J.
Yep...I got this one...I think the problem is easy solved once you embrace relational framework...Answers have been brought to this problem.. I am curious as to what xactly you are trying to establish...

Regard...

Regards... Received on Thu Nov 29 2007 - 01:00:46 CET