Interpretation of Relations

I've been wrestling with the correct interpretation of a relation. I'm currently working under the assumption that a relation comprises both a Type (or header) and a Body (or values).

I'm going to start small.

Consider modelling a situation in which there are people, and they have eye colour. I'm going to define some very small domains, so that I can enumerate the facts that I believe a given relation represents. I'm sorry if the notation is non-standard, but here it is.

Domain D_People = {Joe}
Domain D_Hair = {Red, Blond}

Relation R_People = <<D_People>: {{Joe}}> Relation R_Hair Colour = <<D_People X D_Hair>: {{Joe, Blond}}>

(The bit in the <> is the relation header, the subsequent sets are the relation body).

So, I should interpret this to mean that "Joes hair is blond". But that is not all, because the closed world assumption means that I have another fact (just one, because the domains are so small). This second fact is "NOT Joes hair is red".

And, in particular, it would be wrong to state that

R_Hair Colour: <<D_People X D_Hair>: {}>

indicates that I don't know the colour of Joe's hair. It really means

NOT Joes hair is Red
NOT Joes hair is Blond

Is this right? If so, it leads me to a question about modelling missing information. (And a lot of other questions, too). If not, is there a simple thing that I've missed?

Thanks,
Joe Received on Fri Jan 19 2007 - 02:56:59 CET