Re: Generalised approach to storing address details

JOG wrote:
> vc wrote:
> > JOG wrote:
> >
> >
> > > True, but parents and ancestors are two completely separate relations -
> > > ancestry is transitive, parentage is not for example (my parent's
> > > parent is not in turn my parent too. Well lets hope not eh.). If we
> > > just have a parentage heirarchy, we externally know a semantic
> > > relationship between parentage and ancestry that allows us to infer who
> > > ancestors are - but vitally we are applying two extra inference rule
> > > from our external knowledge:
> > >
> > > 1) Parent(x,y) => Ancestor(x,y)
> > > 2) Ancestor(x,y) & Ancestor(y,z) => Ancestor(x,z)
> >
> > If read as a first-order logic implication, the above does not
> > uniquely define the Ancestor relation.
>
> No, but am I correct in thinking that the above statements could be
> used to define the set of propositions in an Ancestry table via a
> Recursive Definition, with the basis clause referencing the already
> established Parent relation?
>
> > Consider Ancestor(X,Y) = true.
> > If read as a Prolog program, the above is more expressive than any
> > relational algebra query because Prolog has recursion(resolution) and
> > r.a. does not.
> >
> > >
> > > These rules could still be encoded and applied relationally. The tools
> > > do not currently exist to do this without recursive querying, but
> > > (without thinking to hard about it ) I don't envisage a theoretical
> > > reason why they could not be encoded as part of the predicate for a
> > > virtual table, generated from the parentage table itself. Good idea for
> > > a research paper maybe.
> >
> > It has been known for quite a while that the ancestor relation cannot
> > be expressed in f.o.l. and r.a. See "EF - games" in any finite model
> > theory textbook.
>
> This currently is unclear to me - an ancestor relation is a relation
> like any other, and can be enumerated like any other. Take a domain D =
> {grandfather, father, son}. The ancestor relation would be A = {
> (Grandfather, father), (Grandfather, son), (father, son) }. What is so
> inexpressible there? Given that the above is no doubt obvious to you,
> if you have the inclination, perhaps you clarify/expand what you mean
> by "the ancestor relation cannot be expressed in f.o.l. and r.a".

Consider any set of which the ancestor relation is a subset. Any such set is also an "ancestor" relation because it satisfies your definitions. How would you pick up the correct one using only the first-order logic language ?

> Thanks, J.
>
> >
> > >
Received on Thu Dec 14 2006 - 00:06:01 CET