[Om3] binary vs n-ary relations

[Chris Rowley]

Jan 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).

Yes, so would I but only when 'rel' is transtive.  If I saw this
notation used for a non-transitive relation without a good
explanantion then I would suspect that the writer knows little about
what she/he wrote and certainly not what this notation typically
means.

> 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.

This nicely illustrates that it is only use of = as a transitive
relation on a well-deduced set that can really survive this extension.

In this non-transitive (and non-symmetric) use of = for assigment of a
value, I would ask what does 3=x mean?


chris