ions of elements from each set, corresponding
     to "points in space" with coordinates (o,s,i) or ordered triplets,
     which you project on lines, planes --?

Yes, that is a good description of the full product space OxSxI.
A sign relation L, then, is a subset L c OxSxI.
 
JM:  But I believe that it is only begging the question:
     what are S, O, and I?  what are they sets of?
     and why should it matter at all?

I do not understand.  It is a form of description, no more.
It is not meant to tell you