[Om3] binary vs n-ary relations

[Professor James Davenport]

On Wed, 24 Sep 2008, Bruce Miller wrote:
> Professor James Davenport wrote:
> > On Wed, 24 Sep 2008, Paul Libbrecht wrote:
> >> Making them n-ary doesn't solve the classical writing of
> >>  a < b > c
> >> which is used quite often still.
> > Is it? Oh my God ....
> I agree; that's scary!
> OTOH, it is quite common to string different,
> but "consistent", relations together:
>    a = b > c = d >= e >> f
> 
> Sometimes the consistency is dubious:
>    a = b
>      approx c
>      approx d
> (where the approx is indicating that the rhs has
> been somehow approximated, expanded or whatever).
> I've seen cases where it seemed that the d
> was more likely an approximation of a than c!
Indeed so, and therefore it is ahrd to give SEMANTICS to these.
> 
<snip> And then there's the occasional
> 
> Indeed; while I do think it is appealing to be able to
> preserve this notational structure, nary relations
> only scratch the surface.  Short of a contrived
> multi-relation construct, this situation would
> seem to be best solved (at a MML level) by
> a <semantics> pairing of the desired notation
> and the underlying logic, probably using sharing/id/ref.
> 
Indeed so, or some other notational method to be invented, but it's a 
NOTATION, not SEMANTICS.

Michael: I fear you're out-numbered.

James