Re: RM formalism supporting partial information

On Nov 17, 7:54 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
> On 17 nov, 04:35, David BL <davi..._at_iinet.net.au> wrote:

> > Also I think one could argue that the CWA is at odds with a model of
> > partial information, unless you keep in mind the idea of "negation as
> > failure to prove true".
>
> Here we touch the core of why I think your approach is problematic.
> The CWA does apply for the does-not-apply interpretation of null
> values. It does however not apply in its classical form for the value-
> unknown interpretation. Actually Raymond Reiter himself (he introduced
> the CWA) explains very well how it then changes in a paper with the
> title "A sound and sometimes complete query evaluation algorithm for
> relational databases with null values".
>
> What you seem to be doing is mixing the two interpretations, resulting
> in something that IMO doesn't really seem to have any consistently
> meaningful interpretation at all. If you really want to combine the
> two interpretations you need to first define the meaning of a relation
> with null values in terms of sets of "possible worlds" where the null
> values are removed by either giving a concrete value for them or
> declaring them not applicable. That might actually be quite
> interesting, and I don't remember seeing a paper that did this
> properly. Even Zaniolo doesn't really get this right, although he
> claims that he combines the two approaches. So you are in very good
> company. :-)

The two main interpretations of null are apparently

1. value exists but is unknown
2. value doesn't exist

Zaniolo combines these into a single interpretation

   3. no information

I think you're saying 3 is a mixture of 1,2 and doesn't lead to a consistent interpretation. IMO the problem is actually the reverse. It is easy to interpret "no information" (it simply means that the predicate instantiation isn't available for logical deduction), whereas interpretations 1,2 quickly take us outside the realm of the RM/RA. I say that because it seems clear that the RM/RA is only concerned with a strict subset of the FOPL involved with logical deduction from sets of fully instantiated predicates.

There is nothing in RM/RA that's tailored to directly representing sentences like the following

    there exists car C such that owns_car(fred,C).

(which would correspond to interpretation 1 above).

In fact, I would say that the RM can only represent that fact using a new and distinct predicate:

    owns_car_2(P) :- Person P owns a car.

In fact consider the following predicates in Prolog

    owns_car(P,C) :- person P owns car C     owns_car_2(P) :- person P owns a car     person(P) :- P is a person
    car(C) :- C is a car

Note that owns_car_2(P) implies person(P), but the converse is false.

Now consider the following clauses

    owns_car_2(P) :- owns_car(P,C).

    person(P) :- owns_car(P,C).

These are both logically correct. This suggests that my formalism is actually compatible with interpretations 1 and 3. In other words, in the following relation

     Persons     Cars
     ----------------
     fred        c1,c2
     bill

we have a choice about how to interpret the second tuple. This is a semantic on the relation that is outside the mathematical formalism.

What I mean is that we can choose to interpret the second tuple as implying

    owns_car_2(bill) (and therefore person(bill) as well)

or alternatively only

    person(bill)

Moreover, in the second case we can choose to interpret it as implying

    not owns_car_2(bill)

if we choose to apply the CWA.

Obviously the semantic on the relation will affect the data that we're prepared to put into it, and it affects how we interpret the data that we read out of it - particularly when a difference is calculated. However the RM/RA is not itself concerned with the distinction because its rules for logical inference are independent of those semantics.

Am I making sense? Received on Mon Nov 19 2007 - 05:20:09 CET