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

On Friday, December 18, 2015 at 11:25:35 AM UTC-8, Tegiri Nenashi wrote:
> On Friday, December 11, 2015 at 10:45:15 AM UTC-8, Nicola wrote:
> > 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
> Norbert Sausage
>
> 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
> Norbert Ball
>
> Here is what projection of this relation to {topological_object} might look like:
>
> topological_object
> ------------------
> Dohnut
> Ball
>
> 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.

Here is less sloppy way to express my discomfort.

When describing relational model (and its extensions) you are required to describe the following.

1. What are the objects that we operate with.

In classic relational theory they are -- relations. Next, we describe relation structure in terms of attributes, and tuples.

In Kanellakis generalized relational model the objects are semi-algebraic sets, although the importance of attribute naming is glossed over.

One can also operate algebraic sets (geometric varieties) and their counterparts (algebraic ideals). My impression is that algebraic geometry is far more advanced compared to the theory of semi-algebraic sets.

Please note that in all three cases given a relation, one can easily tell what attributes of that relation are. I'm not sure I can confidently exhibit attributes in the examples provided by Norbert.

2. What are relational operators between the objects.

This is usually accomplished in terms of relations structure, for example natural join in classic relational theory produces a relation with a set of attributes which is the union. Next, the tuples of the resulting relation are constructed as ...

In case of algebraic sets there are operations that mimic classic relational algebra, and this is why such extension of relational model is possible.

In the case of topological extension Norbert listed operations which are counterparts of relational, but those are operations over entire topologies. My understanding is that topology is dimension unaware; so when working with topologies how does one identifies attributes/variables? Received on Fri Dec 18 2015 - 22:56:17 CET