[om] semantics of n-ary xor?

[Andreas Strotmann]

Thanks, David!

David Carlisle wrote:

>>Now I ask you:  what exactly *is* the meaning of n-ary xor in MathML (or 
>>OpenMath, for that matter)?
>>    
>>
>
>We did discus this at some length in an OM meeting somewhere, the result
>is that OM and MathML are consistent here:
>
I've clearly been missing too many of those meetings...  Sorry for 
bringing up an old hat then.

>Openmath says (logic1 CD)
>
><Description> 
>This symbol represents the logical xor function which is an n-ary
>function taking boolean arguments and returning a boolean
>value. It is true if there are an odd number of true arguments or
>false otherwise.
></Description>
>
>MathML says (C.2.3.15)
>
>The is the n-ary logical "xor" operator. The constructed expression has
>a truth value of true if an odd number of its arguments are true.
>
I think this should be put in the corresponding section of chapter 4, 
too, then.  (Sorry, I hadn't started working on proof-reading Chapter C 
yet when I wrote this).

>We did find some references to support this definition, but I don't have
>them to hand at present, perhaps James or Stan can cite something?
>

Oh, this is clearly the "logical" extension of the original binary xor, 
so I'm not surprised you'd find a document specifying it this way.  The 
argument why the other "common sense" definition might be better would 
probably not turn up in the context of such a book, since the "big" 
version of that xor, exists-uniquely, is not always actually written as 
one (though sometimes it is -- come to think of it, several professors 
at my university actually did teach it during my undergrad math years - 
they preferred the big-or notation for exists, too).

Anyway, this is no problem as long as there is a specific definition one 
way or the other.  The "other" reading of an n-ary xor can always be 
provided under another symbol name (external to MathML, "internal" to 
OpenMath).  It's just too bad that only that "other" reading  gives a 
really nice "big" version.

 -- Andreas
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