[Om3] binary vs n-ary relations

[Professor James Davenport]

On Wed, 24 Sep 2008, Jan Willem Knopper wrote:
> Chris Rowley wrote:
> I would assume a rel b rel c is almost the same as a rel b and b rel c
> (where rel is a relation).
I would claim that it is EXACTLY the same (and therefore redundant). I do 
not know where it conveys different information, and if it does, it 
certainly needs documenting, so Michael's "making them n-ary" doesn't 
work. 
> > Although one conventionally strings infix order relations together as
> > if they might be n-ary I see this as a typical abuse of the notation
> > for relations.
> 
> The use and meaning I can see is formula manipulation. When solving an
> exercise by formula manipulation, one would use n-ary relation symbols
> (for example (x+1)^2=(x+1)*(x+1)=x^2+x+x+1=x^2+2x+1).
> This is semantically different from a system of exercises: 3=x and x=2
> would never be written as 3=x=2.
I'm not sure I follow this.
> At the moment we use the n-ary eq: eqs, which locally is placed in the
> 'hidden' cd relation2 (eqs) and on the OpenMath website in the
> experimental relation4 (eqs).
As I said, I'm not sure I understand why you would want the SEMANTICS of 
this, as I am not sure what they are.
James