Re: Generalised approach to storing address details

From: vc <boston103_at_hotmail.com>
Date: 15 Dec 2006 13:26:34 -0800
Message-ID: <1166217994.524776.76290@73g2000cwn.googlegroups.com>

JOG wrote:
> vc wrote:
> > JOG wrote:
> [snips]
> > >
> > > 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 ?
> >

>

> Well thanks for reiterating this (and Marshall for his clear
> explication). And yes, I understand that without recursion the RA is
> unable to generate transitive closure. However I was more interested in
> a response to the following:

>

> JOG wrote:
> > vc wrote:
> > > JOG wrote:
> [snips]
> > > > 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?"

F.o.l. does not allow circular definitions: P(x, y) =def. ...P(..) would be ill-forme -- P cannot appear on the right.

>

> In prolog I think I can state those rules as: "ancestor(A,D) :-
> father(A,D)." , "ancestor(A,D) :- father(F,D), ancestor(A,F)." and it
> will generate the inferences for me.

Prolog allows circular definitions because Prolog is an extension of a specific fragment of f.o.l. and can handle such definitions with its SLD engine, but not very well, for example your older definition, although "theoretically" correct, will lead to an infinite recursion.

>Now the RM is not an inference

> engine like Prolog, it's a database. But I see no theoretical reasons
> why I could not do the equivalent

There are equivalents e.g. Oracle's "connect by" or Date's transitive closure operator.

>equivalent via a RDBMS by setting up a

> "recursive definition" for an Ancestors relation (perhaps via the DDL)
> - a virtual relation that depends on the parents relation for its
> derivation.

I do not understand what you suggest. Received on Fri Dec 15 2006 - 15:26:34 CST