SUO: Re: Lations -- Eternal Subspecies & Secular Kifilians
pat hayes wrote:
>
> > Horn, Graham wrote:
> > >
> > > Dear Matthew,
> > >
> > > Thanks for this explanation.
> > > I certainly agree about the
> > > restrictions with 3D models
> > >
> > > However, I still don't understand why relations
> > > do not also have a time dimension. For example,
> > > what about two beings which have friendly relations
> > > at some periods and hostile ones at other times?
> > > Other such relations that come to mind include:
> > > trade, communication connections and schedules
> > > (eg. road, rail, cable), treaties, taxation and
> > > social security - all possibly with time-varying
> > > capacities, many of which were exemplified in the
> > > last century by the impacts of technology and/or
> > > the Iron Curtain.
> >
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> >
> > Graham,
> >
> > Brief note for now, as I am in the mi(d)st of a lot (49) of other work --
> >
> > A k-adic (-ary, -valent) relation with a time dimension adjoined
> > is just a special kind of a (k+1)-adic (-ary, -valent) relation.
>
> That is one way to think about it. Another is that is a binary relation
> between an assertion involving a k-ary relation and a time. Another is
> that is is a k-ary relation between things which are unary functions of
> times. And there are other ways, all of which give different ontological
> frameworks and different axiomatic styles.
>
> Of course, if we were using a higher-order logic
> in which the comprehension inference rule were valid,
> then these would all be equivalent; but in first order
> they are distinct.
>
> Pat Hayes
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Pat,
The application of my statement was restricted, perhaps too implicitly,
to the sorts of extensional examples of relations that are relevant to
ordinary relational databases, but perhaps it would do us all some good
if you could elaborate on the subtleties to which I can but dimly sense
that you are alluding here.
Thanks In Prospect,
Jon Awbrey
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