Re: Comments on Norbert's topological extension of relational algebra

On Friday, December 11, 2015 at 10:45:15 AM UTC-8, Nicola wrote:
> Norbert may have better arguments, but what I find it intriguing in his
> approach is that you store
> the *whole* topology of the *whole* space potentially in a cheap and
> simple way. As far as I know,
> in DE-9IM (based on Egenhofer's ideas) you may model the relationship
> between two objects with one
> 3x3 matrix, but storing a matrix for each possible pair of objects (or
> for a subset big enough to
> reconstruct the whole topology) is most likely impractical. Hence, such
> matrices are usually used
> to infer the topological relationships between objects from geometric
> data (e.g., see
> ST_Relate() in SQL/MM). Besides, Norbert's model provides a way to
> build new topological spaces
> from existing ones using well-founded well-known constructions. This is
> a feature I have not seen
> elsewhere (not that I know all models out there, though). It might
> still be infeasible in practice,
> given that there are transitive closures to compute here and there, but
> it has some potential.
>
> Btw, I have found that this paper provides a less formal but way more
> accessible introduction to the
> topic:
>
> https://www.academia.edu/364355/Geometrical_and_Topological_Approaches_In_Building_Information_Modelling

I'm still wanting an example that might clarify topological extension of RA. If the proposal is about introducing topological datatype, then the extension is quite intuitive, and can explained to database person in terms of tuples and attributes.

The first question is what are the values of topological datatype. I assume, they are certainly not entire topologies. They are geometric objects with "qualitative" description, so that for example cube is not distinguishable from sausage. "Topological datatype" means that those objects are from the same topological space; in the same venue as values from ordinary datatypes are chosen.

Consider the following relation FavoriteShapes(name, topological_object):

name topological_object

--------   ------------------
Jan        Dohnut
Nicola     Cube

Actually, if one agrees how to choose a representative in every class of all topologically equivalent objects, then the FavoriteShapes relation has to be rewritten as

name topological_object

--------   ------------------
Jan        Dohnut
Nicola     Ball

Here is what projection of this relation to {topological_object} might look like:

topological_object

I suspect this is not direction where Norbert is going. For once he considers interactions between two topological spaces (e.g. product topology) and I fail to see how this can be cast in relational terms. Received on Fri Dec 18 2015 - 20:25:34 CET