[Om3] binary vs n-ary relations

[Jan Willem Knopper]

Chris Rowley wrote:
> 
> > In the OpenMath CD relation1.ocd most of the relations are given as
> > binary (e.g. eq, lt, gt, leq, geq) and in the MathML2 spec they are
> > given as n-ary. What do we do?
> > 
> > In this case, I think that the soluton should be make them n-ary.
> 
> When I saw the order relations being n-ary my reaction was 'what does
> that mean?': I may have mentioned this as a question in my earlier notes.

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).
> 
> 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.

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).
> 
> To exactly what subset of S^3 does the possible 3-ary relation given
> by this notation correspond?  Remember that to make general sense of
> this notation we need to define this for all relations, not just
> transitive ones.
> 
> Also there is no question of associativity here since, in general, (a < b) < c  
> is meaningless (neither true nor false).
> 
> > I have started a discussion item on the discussion page at
> > http://wiki.openmath.org/?title=cd%3Arelation1.
> 
> So I guess that is where this message sould go too.  Hmm, I tried, but
> it turns out that my first trial of Swim has not been successful.
> Will try and get my head around that later.
I have posted something there on Monday, but I can't find the page any
more, so I've mailed it instead.

Regards,

Jan Willem
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: application/pgp-signature
Size: 195 bytes
Desc: not available
Url : http://openmath.org/pipermail/om3/attachments/20080924/f0d072db/attachment.pgp