[Om3] Symbol Definitions in the Description elements

[Professor James Davenport]

On Wed, 17 Sep 2008, Chris Rowley wrote:
> With this hat on I am currently not agreeing with your conclusions
> about the necessity of 'uniqueness' at the end.  It seems to me that,
> pragmatically if not formally, it is no more difficult to make a
> 'human check' on the 'mathematical consistency' of two practical
> definitions than it is to check that there are no cycles in 'the
> dependency graph' starting a definition or that a recursive definition
> gives a computable function.
> 
> Thus I would allow multiple definitions but insist that they are
> compatible.
A plausible point of view. It makes the concept of non-cyclicity 
non-deterministic, since it might depend which definitions one used: I 
would wish to insist on NEVER CYCLIC. 
> Moving on, one could usefully insist on a _mathematical_ proof of all
> of such things: compatibility, non-cyclicity, finiteness etc.  Or not!
Non-cyclicity is a feature of the entire graph of CDs, and therefore 
subject to change, whereas consistency of definitions in a CD is a fact of 
that CD (assuming that the SEMANTICS, as opposed to the way they are 
expressed, of objects depended on does not change, and this is illegal).
James