>RE interoperability between CAD, BIM, GIS I think many processes being
>developed for physical space could applied to semantic space at the
>same time. (01)
Hmm. While I don't want to rain on anyone's parade, let me suggest
that this particular overloading of "space" might be misleading.
Physical space has a very special structure: it is 2- or 2.5- or
3-dimensional, usually taken to be continuous or very close to it,
often treated as a subset of R|n, has a meaningful topology and
mereology, supports a variety of well-known algebras, etc.. But none
of this applies to semantic "space". Or perhaps better, there isn't
any evidence that any of it applies to semantic space, because nobody
has a really convincing notion of what semantic space is really like.
The best (ie not so obviously inadequate as the others) notions seem
to involve not a continuous topological space but something more like
a lattice (cf. the WordNet hypernym/hyponym structure) or a
relational algebra (databases) or relational structure (logical
concept models). Now, all of these can be called "spaces" in some
mathematical sense, but that doesnt mean very much since almost
anything with a structure can be called that, and the various
mathematical senses are very different, and support very different
kinds of mathematics. For example, basic topological facts like the
Jordan curve theorem (to get from inside to outside, you have to pass
through the boundary) are just plain false in lattices and relational
models. (02)
Still, all that said, if you CAN find useful cross-overs, I agree
they would be great to have. (03)
Pat Hayes (04)
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