Re: Inference for error checking [was Re: How to avoid that collections "break" relationships]

[David Booth]

On 04/06/2014 09:07 PM, Peter F. Patel-Schneider wrote:
Well, certainly, one could do this if one wanted to.  However, is this a
useful thing to do, in general, particularly in the absence of
constructs that actually sanction the inference and particularly if the
checking is done in a context where there is no way of actually getting
the author to fix whatever problems are encountered?

I'll let others judge that.  My goal in the example was simply to 
demonstrate how it *could* be useful.


My feelings are that if you really want to do this, then the place to do
it is during data entry or data importation.

Sure, it's certainly best to do error checking as early as possible, but 
often there is still some value in doing it later as well.  Maybe the 
data users can contact the data publishers and alert them to a potential 
problem?  But like I say, I'll let others judge its usefulness.  I don't 
have a strong opinion on that.

David



peter

On 04/03/2014 03:12 PM, David Booth wrote:
First of all, my sincere apologies to Pat, Peter and the rest of the
readership for totally botching my last example, writing "domain" when
I meant "range" *and* explaining it wrong.  Sorry for all the
confusion it caused!

I was simply trying to demonstrate how a schema:domainIncludes
assertion could be useful for error checking even if it had no
formal entailments, by making selective use of the CWA.  I'll
try again.

Suppose we are given these RDF statements, in which the author
*may* have made a typo, writing ddd instead of ccc as the rdf:type
of x:

  x ppp y .                       # Triple A
  x rdf:type ddd .                # Triple B
  ppp schema:domainIncludes ccc.  # Triple C

As given, these statements are consistent, so a reasoner
will not detect a problem.  Indeed, they may or may
not be what the author intended.  If the author later
added the statement:

  ccc owl:equivalentClass ddd .   # Triple E

then ddd probably was what the author intended
in triple B.  OTOH if the author later added:

  ccc owl:disjointWith ddd .      # Triple F

then ddd probably was not what the author intended
in triple B.

However, thus far we are only given triples {A,B,C}
above, and an error checker wishes
to check for *potential* typos by applying the rule:

  For all subgraphs of the form

    { x ppp y .
      ppp schema:domainIncludes ccc . }

  check whether

     { x rdf:type ccc . }

  is *provably* true.  If not, then fail the
  error check.  If all such subgraphs pass, then
  the error check as a whole passes.

Under the OWA, the requirement:

     { x rdf:type ccc . }

is neither provably true nor provably false given
graph {A,B,C}.  But under the CWA it is
considered false, because it is not provably true.

This is how the schema:domainIncludes can be
useful for error checking even if it has no formal
entailments: it tells the error checker which
cases to check.

I hope that now makes more sense.   Again, sorry to
have screwed up my example so badly last time, and
I hope I've got it right this time.  :)

David


On 04/02/2014 11:42 PM, Pat Hayes wrote:

On Mar 31, 2014, at 10:31 AM, David Booth <da...@dbooth.org> wrote:

On 03/30/2014 03:13 AM, Pat Hayes wrote:
[ , . . ]
What follows from knowing that

ppp schema:domainIncludes ccc . ?

Suppose you know this and you also know that

x ppp y .

Can you infer x rdf:type ccc? I presume not, since the domain might
include other stuff outside ccc. So, what *can* be inferred about the
relationship between x and ccc ? As far as I can see, nothing can be
inferred. If I am wrong, please enlighten me. But if I am right, what
possible utility is there in even making a schema:domainIncludes
assertion?

If "inference" is too strong, let me weaken my question: what
possible utility **in any way whatsoever** is provided by knowing
that schema:domainIncludes holds between ppp and ccc? What software
can do what with this, that it could not do as well without this?

I think I can answer this question quite easily, as I have seen it
come up before in discussions of logic.

...

Note that this categorization typically relies on making a closed
world assumption (CWA), which is common for an application to make
for a particular purpose -- especially error checking.

Yes, of course. If you make the CWA with the information you have, then

ppp schema:domainIncludes ccc .

has exactly the same entailments as

ppp rdfs:domain ccc .

has in RDFS without the CWA. But that, of course, begs the question.
If you are going to rely on the CWA, then (a) you are violating the
basic assumptions of all Web notations and (b) you are using a
fundamentally different semantics. And see below.

None of this has anything to do with a distinction between entailment
and error checking, by the way. Your hypothetical three-way
classification task uses the same meanings of the RDF as any other
entailment task would.


In this example, let us suppose that to pass, the object of every
predicate must be in the "Known Domain" of that predicate, where the
Known Domain is the union of all declared schema:domainIncludes
classes for that predicate.   (Note the CWA here.)

Given this error checking objective, if a system is given the facts:

  x ppp y .
  y a ccc .

then without also knowing that "ppp schema:domainIncludes ccc", the
system may not be able to determine that these statements should be
considered Passed or Failed: the result may be Indeterminate.  But
if the system is also told that

  ppp schema:domainIncludes ccc .

then it can safely categorize these statements as Passed (within the
limits of this error checking).

Why? [ y a cc . ] does not follow from this assertion and the x ppp
y, so this looks like an Indeterminate to me. Even with the CWA
applied to ppp, your check here is extremely risky. In fact, I could
invoke Gricean reasoning to conclude that the domain of ppp **almost
certainly must** include something outside ccc; because if not, why
did whoever wrote this use the more cautious schema:domainIncludes
rather than the simpler and more direct rdfs:domain? Indeed, isnt the
ubiquity of the OWA in Web reasoning the only justification for
having a construct like schema:domainIncludes at all? Why else was it
invented, if not to allow for further information to make the domain
larger?

Thus, although schema:domainIncludes does not enable any new
entailments under the open world assumption (OWA), it *does* enable
some useful error checking inference under the closed world
assumption (CWA), by enabling a shift from Indeterminate to Passed
or Failed.

I would not want any important decision to rest on such an extremely
flaky foundation as this.


If anyone is concerned that this use of the CWA violates the spirit
of RDF, which indeed is based on the OWA (for *very* good reason),
please bear in mind that almost every application makes the CWA at
some point, to do its job.

Um, bullshit. But in any case, even if it were true, the important
thing is to know when to invoke the CWA. Assuming that you know all
the domain, when you have been told explicitly that you probably have
not been told all of it, is a very bad heuristic for invoking the CWA.

Pat


David



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