From: Andreas Strotmann <Strotmann@rrz.uni-koeln.de>

Date: Wed, 17 Sep 2003 17:25:34 +0200

Message-ID: <3F687CEE.50800@rrz.uni-koeln.de>

To: David Carlisle <davidc@nag.co.uk>

Cc: om@openmath.org, www-math@w3.org

Date: Wed, 17 Sep 2003 17:25:34 +0200

Message-ID: <3F687CEE.50800@rrz.uni-koeln.de>

To: David Carlisle <davidc@nag.co.uk>

Cc: om@openmath.org, www-math@w3.org

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. -- AndreasReceived on Wednesday, 17 September 2003 11:25:39 UTC

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