Re: So let me get this right: (Was: NFNF vs 1NF ...)
Date: Sun, 13 Feb 2005 14:12:51 GMT
Message-ID: <DfJPd.10829$dO7.731251_at_phobos.telenet-ops.be>
Paul wrote:
> Jan Hidders wrote:
>> Paul wrote: >> >>> What would an untyped RVA be, and how could they lead to Russell's >>> paradox? >> >> An untyped RVA is an RVA that can contain any finite or infinite >> relation.
>
> OK so for a typed RVA you are specifying the exact predicate i.e. all
> the RVA's internal column names and types, and every RVA in that column
> has to have the same internal columns?
Yes. Although, if you allow variant types or union types such that they can have different fields and then they would allow that and still be typed. But they should all be described by a single type. That's what it means to be typed.
> But for an untyped RVA, you could have one row with an RVA that has only
> one integer column, and an RVA in a different row but same column that
> has two char columns, etc?
Yes, you could, although, as I just said, you can already have that in a typed setting. And to make things even more confusing, even if you disallow that you could still get the paradox.
>>> I thought that you could only get Russell's paradox if you allowed >>> RVAs to be relation variables rather than relation values? >> >> In the original naive set theory in which the paradox was formulated >> there is no notion of variable, just values.
>
> But to get Russell's paradox you essentially need to be able to refer to
> a set that can contain itself. In other words, we need to be able to
> express the idea of a relation containing a copy of itself as an
> attribute in one of its rows.
>
> I don't see how this is possible using relation-values, and given that
> relations are finite and explicitly enumerated row-by-row. You can only
> start to concieve of the idea of a relation containing itself if it's
> infinite, surely?
I don't agree that the relational model disallows infinite relations or requires explicit enumeration. But the point was that even if that is allowed and even if you drop typing, which is really not a big restriction in practice, there is *still* no unavoudable problem from a theoretical point of view. The fact that you apparently cannot even conceive how a model that does this looks or what it might mean demonstrates nicely how exotic the versions of the relational model are that we are looking at here.
- Jan Hidders