Chris Rowley wrote: > > > In the OpenMath CD relation1.ocd most of the relations are given as > > binary (e.g. eq, lt, gt, leq, geq) and in the MathML2 spec they are > > given as n-ary. What do we do? > > > > In this case, I think that the soluton should be make them n-ary. > > When I saw the order relations being n-ary my reaction was 'what does > that mean?': I may have mentioned this as a question in my earlier notes.
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). > > Although one conventionally strings infix order relations together as > if they might be n-ary I see this as a typical abuse of the notation > for relations. 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. At the moment we use the n-ary eq: eqs, which locally is placed in the 'hidden' cd relation2 (eqs) and on the OpenMath website in the experimental relation4 (eqs). > > To exactly what subset of S^3 does the possible 3-ary relation given > by this notation correspond? Remember that to make general sense of > this notation we need to define this for all relations, not just > transitive ones. > > Also there is no question of associativity here since, in general, (a < b) < > c > is meaningless (neither true nor false). > > > I have started a discussion item on the discussion page at > > http://wiki.openmath.org/?title=cd%3Arelation1. > > So I guess that is where this message sould go too. Hmm, I tried, but > it turns out that my first trial of Swim has not been successful. > Will try and get my head around that later. I have posted something there on Monday, but I can't find the page any more, so I've mailed it instead. Regards, Jan Willem
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