Re: RM formalism supporting partial information

On Nov 17, 8:18 am, paul c <toledobythe..._at_ooyah.ac> wrote:
> David BL wrote:
>
> > Eg
> > r =
> > {
> > (names={fred, bill}, cars={c1}),
> > (names={}, cars={c2})
> > }
>
> > then the information content is associated with all the following
> > propositions
>
> > person(fred).
> > person(bill).
> > owns_car(fred,c1).
> > owns_car(bill,c1).
> > car(c1).
> > car(c2).
> > ...
>
> (I take it that r here has two tuples. I've been a little confused by
> the parentheses.)

Yes.

> I would like to know what it would mean to "insert"
> (names{joe}, cars{c2}) to r, or if you prefer, to union that and r.

> If it is possible in your "interpretation", what would the resulting "r"
> look like?

    r' =
    {

        (names={fred, bill}, cars={c1}),
        (names={}, cars={c2}),
        (names={joe}, cars={c2})

r' has 3 tuples and its information content is

    person(fred).
    person(bill).
    person(joe).
    owns_car(fred,c1).

I think of this set of propositions as "inhomogeneous" because they don't all share the same header.

Note that the tuple (names={}, cars={c2}) in r' is redundant and could be removed without affecting the meaning.

The definition of r1 <--> r2 formalises the idea of equivalence classes and is intended to address the non-uniqueness of representation. This is analogous to equivalence classes for fractions. Non-uniqueness of representation is annoying but hardly a show stopper.

Union, intersection and difference operations on relations can all be easily defined as the corresponding operations on the sets of inhomogeneous propositions. Therefore it is possible to think of these operators as being defined on the equivalence classes.

However a difference operator is a little tricky because one could argue that

    owns_car(fred,c1) => person(fred)

so therefore we have the contrapositive

    not person(fred) => not owns_car(fred,c1)

So if from r' we subtract a relation that implies person(fred) we perhaps should really remove the proposition owns_car(fred,c1) as well. In the MS word document I defined two difference operators to investigate this curious idea.

I guess this moves into the arena of deductive databases. Received on Sat Nov 17 2007 - 06:11:11 CET