On 28 nov, 15:05, "David Cressey" <cresse... (AT) verizon (DOT) net> wrote:
Exactly. An which interpretation applies determines which CWA should
be assumed.

Yes, it can be.

-- Jan Hidders

On Nov 29, 12:15 am, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote:
The concept of "possible answers" isn't universally applicable, and
therefore seems to represent quite a problem for any model of partial
information that emphasises that concept as fundamental.

Did you read my response to Brian regarding the approach to absorb the
CWA/OWA distinction into the intensional definitions?

What do you think of the suggestion that the formalism (which is
concerned with extensions rather than intensions)

1) ignores the CWA/OWA distinction;

2) assumes the CWA applies everywhere; and

3) null is *always* interpreted as non-existence w.r.t.
the (carefully worded) intensional definitions?

This approach seems simple and self consistent. In fact I think it
gives the best of both worlds - it becomes

a) Zaniolo's interpretation of no-information when the
OWA applies in the intensional definition; or else

b) (actual) non-existence when the CWA applies in the
intensional definition.

It doesn't however, attempt to model the case of "value exists but is
unknown". IMO that case should be modeled *explicitly* with a
different predicate. More specifically I would say a distinct base
relvar is required.

As an example suppose we have the predicate owns_car(Person,Car), and
we want to be able to record persons that are known to own some
unknown car. That implies that the intensional definition of
owns_car has an OWA. Therefore we introduce a distinct base relvar
owns_some_car(Person) that must satisfy the following integrity
constraint

owns_car(Person,Car) => owns_some_car(Person)

However the converse is false because of the OWA nature of
owns_car(Person,Car). As a result owns_some_car(Person) is not equal
to a projection on owns_car(Person,Car).

It is interesting to note that the intensional definition of
owns_some_car can itself involve an OWA.

On 29 nov, 03:54, David BL <davi... (AT) iinet (DOT) net.au> wrote:
The concept of 'possible answers' applies and is well defined for all
databases where you have precisely defined what it means if certain
data is missing, and note that his includes the definition that says
that it means nothing. So what you mean by "isn't universally
applicable" is completely beyond my comprehension.

Yes, I did. Typical case of "let's redefine our terminology to make
the problem go away". :-) It won't do.

If I ignore for the moment 1) (because 1) and 2) seem contradictory
because I cannot assume there is no difference between X and Y and at
the same time assume that only Y applies everywhere) this is just the
classical value-does-not-apply interpretation.

Sure, the value-does-not-apply interpretation can always also be
represented without null values.

The thing is that you have now fully ignored the real problem of
incomplete information which is that in practice the CWA does not
always fully apply. Your main solution seems to be to redefine the
meaning of the relations such that it does, which, of course, doesn't
solve anything at all and simply puts the problem back on the plate of
the user.

-- Jan Hidders

On Dec 1, 12:48 am, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote:
Consider the following predicates, all with OWA intensional
definitions

age(Person,Age)
occupation(Person, Occupation)
married(Person,Person)
died(Person,Date)

You say the concept of possible answers is well defined. How exactly
would you calculate the possible 27 year old pilots? What does it
mean precisely?

I meant that the actual CWA/OWA distinction is absorbed into the
intensional definition, so that it can be assumed that with respect to
the intensional definition the formalism assumes a CWA. I thought
that was clear.

You say "of course doesn't solve anything at all" without giving any
hint at all why you say that. Can you elaborate?

What problem doesn't it address? Can you provide a specific example?

On 1 dec, 04:17, David BL <davi... (AT) iinet (DOT) net.au> wrote:
You seem to assume that "well defined" and "can be computed" is the
same, which it isn't. But to answer your question, assuming that
everybody has only one occupation that would be every person p for
which there is no tuple (p, a) with a<>27 in relation age, and no
tuple (p, o) with o<>"pilot" in relation occupation. If the domain of
Person is not finite, or restricted by a relation person(Person) then
the result may be infinite.

It contains every person that might be a 27 year old pilot as far as
the given database is concerned.

It was.

Suppose you have a table R(a,b,c) with candidate key {a} where column
c may contain null values that indicate that we don't know it's value.
You can now solve this by splitting this into R1(a,b) and R2(a,c) and
thus remove the null values. It could be that R was, apart from the
null values, complete so that would mean that the CWA applies to R1,
but not to R2. So it will be the case for some queries over R1 and R2
that when computed in the usual way they return the exact answer, some
will return the possible answers, and some will return neither.
Wouldn't it be nice if the DBMS could tell you which ones do what? Or
if you could tell the DBMS that it shouldn't compute the query as
given but rather such that it return the set of possible (or certain)
answers for the given query, if it can?

-- Jan Hidders

On Dec 2, 9:22 pm, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote:
Indeed in the example there is no person(Person) and no CWA specified
to limit what's possible. This raises questions like: Should
"possible" include people in the distant future? Should it include
alternative realities (if one accepts the Many Worlds Interpretation
(MWI) of Quantum Mechanics)? What about a person described in a work
of fiction?

Do you still say it is "well defined"?

What do you mean by "as far as the given database is concerned"?
Surely that can only be regarded as CWAs on various intensional
definitions of the predicates?

I think if we have the proper intensional definitions in mind, and
assume every relation has a CWA then we will easily be able to
interpret a query correctly.

Eg R1(a,b), and R2(a,c) are

employee(Person,Date) <=>
Person is current employee of company X who commenced on Date.

address(Person,Address) <=>
It is known that Person lives at Address

then, as an example { P | employee(P,D) } \ { P | address(P,A) } can
be interpreted as (all) the persons that currently work for company X
that don't have a known address.

It seems to me there can be lots of subtle variations in the
intensional definitions, such as the way employee(P,D) mentioned
company X whereas address(P,A) did not. This makes me skeptical
whether a DBMS will be able to formalise it, beyond simply allowing
the user to define a schema, support the RA, allow for integrity
constraints etc

On 3 dec, 02:51, David BL <davi... (AT) iinet (DOT) net.au> wrote:
But a type or domain will have been associated with the column. That
defines the upper bound of the possibilities.

Of course. This is not some terminology I made up, it's well
established in the literature.

That the database contains no information that logically implies the
opposite.

Not if you use those terms in their usual meaning.

This smells a bit tautological. Unless you specify what "it is known
that" means more precisely it might very well be "is in the address
table" in which case this would be meaningless statement.

Formalizing that can in general be done by formulating a constraint
over two databases d and d' with the schema, where d represents the
actual database and d' the ideal correct database. In general that is
too powerful so various more restricted ways of doing that are under
research at the moment. One you have already formulated yourself,
i.e., declaring that the CWA appplies to certain views, and the other
is in terms of a relation R and a query Q over the ideal database that
returns a result with the same header and the interpretation that R is
complete for the tuples in Q.

-- Jan Hidders

On Dec 4, 2:32 am, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote:
Ok, I understand now. I agree it is well defined.

I can see it is quite useful when the domain has a small cardinality,
such as a fixed enumeration of colours. How is the definition useful
for a string or numerical domain? Clearly reporting the possible
answers is impossible where infinite, and silly where finite but
extremely large - such as the case when a string domain constrains the
maximum number of characters.

Agreed.

Please substitute "... it is currently known to the company X HR
department that ..."

If I get the chance I'll read more of the literature on CWA. Sometime
I want to look at Reiter's work.

On 4 dec, 02:48, David BL <davi... (AT) iinet (DOT) net.au> wrote:
*phew* :-)

It's main role is just as the logical counterpart of the set of
certain answers and the set of impossible answers. In the sense that
you use "useful" here the set of certain answers is certainly much
more directly useful. However, if the query for the possible answers
is domain dependent then the DBMS could warn you about this, indicate
the problem and ask you to reformulate the query slightly such that is
isn't. In your example this could be done by restricting the set of
possible persons to those in a certain relation for which the CWA
holds. I'd suggest that in practice that is often what you want
anyway.

-- Jan Hidders