[Om3] binary vs n-ary relations

[Michael Kohlhase]

Professor James Davenport wrote:
> 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.
>   

one way to do this is to appeal to a variant notation definition by
placing @variant attributes strategically. For instance, if we have the
pragmatic a = b = c which would be represented as  a = b /\ b=c, then we
could have a variant="chaineq" on the and at logic1 symbol and on the
second eq at relation1 symbol, telling the renderer not to render the /\
and for the = not to render the first argument. The only problem I see
here is how to get the <mrow>s right.

Michael

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