[Om3] binary vs n-ary relations

[Chris Rowley]

I shall try to be brief here but I think there is a wider issue that
questions about this particular notation brings to the surface.

As with many parts of mathematics, exactly what is written with
non-text symbols and what is written using natural language (or
various mixtures, of course) is very arbitrary.  It varies from
(mathematical) culture to culture and over time.  Also, the range of
symbols and constructions available varies.

Jan's 'problem' is that he has to 'deal with' any notation that comes
from a particular culture right now; but (and this is the real
strangeness) he is not expected to 'deal with' the many ideas
(expressable as OpenMath symbols, operators etc.) from that same
culture that are always expressed purely in natural language, no
symbols needed (used).

That this distinction is unnautural is well illustrated by the fact
that spoken maths does not make any distinction (almost:-) between the
two classes.  

Discusss!


chris



Jan

> Paul Libbrecht wrote:
> > 
> > Le 25-sept.-08 à 11:14, Jan Willem Knopper a écrit :
> ...
> > > There are no obvious semantics differences here, and I am not sure
> > > enough that I actually need anything like the semantics of a formula
> > > manipulation.
> > 
> > I think the ball is on your side Jan Willem... many users and user- 
> > guides (e.g. teachers) will want something to look like a<b<c and  
> > other such...
> 
> The main problem is indeed with parsing and notation.
> 
> What I want is an easy way to parse this. 
> 
> With the OpenMath currently suggested for a=b=c (namely a=b/\b=c) I will
> have to check whether the OpenMath subexpression is "the same" for the
> b's (that is strip whitespace around XML elements, possibly strip spaces
> inside OMIs, and string-compare the result). 
> 
> Another option would be to compare available output of the partial
> expressions (which could be an internal semantic tree, or mathml-p, or
> ...), but this might not always give the desired result.
> 
> > - how are you going to offer this to users ? (e.g. wiris input editor
> > does it by reparsing the mathml-p)
> 
> Probably the user wants a choice on what OpenMath they get from a=b=c.
> In my editor I have binary and n-ary infix symbol and they are parsed
> such that a+b+c is (a+b)+c, a=b is binary and a=b=c is n-ary. The user
> can enter them typing or inserting the symbol several times.
> 
> The nicest would probably be to have an option in the editor to get the
> output I like, (for our software) or the official ouput, (for other
> users of the editor). When using an attribution this might be easier.
> 
> To input a=b=c from OpenMath in the editor, or to show a=b=c in a
> webpage I would probably require users to use "my" format, otherwise
> it would be shown unchanged as a=b/\b=c.
> 
> > - how are you going to express the underlying OpenMath (as above I  
> > suppose)
> One solution is to use some private OpenMath symbol(s) which probably
> won't make it to OpenMath 3/MathML 3. 
> 
> Another option could be to add some attribute to the application of the
> and, indicating that it should be possible to display the expression
> differently. 
> The advantage of this would be that the OpenMath is the same and should
> be handled the same by other programs. The disadvantage is that we
> currently do not always have support for OMATTR attributes (is
> annotations1 defined somewhere ? It is mentioned in the standard as an
> example for OMATTR, but I couldn't find a CD online). 
> Another disadvantage is that a OMATTR symbol that shouldn't be there
> would might the meaning (am I really going to do all the checks required
> for the meaning to stay the same?).
> 
> > 
> > I think the first question is crucial and needs an elaborate answer  
> > much further than "just apply this symbol here" as is done with most  
> > "simple application symbols".
> > It probably is a general issue of binary operators.
> 
> 
> Jan Willem