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

On 03/31/2014 11:59 AM, Peter F. Patel-Schneider wrote:
>
> On 03/31/2014 08:31 AM, David Booth 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.
>>
>> Entailment produces statements that are known to be true, given a set
>> of facts and entailment rules.  And indeed, adding the fact that
>>
>>   ppp schema:domainIncludes ccc .
>>
>> to a set of facts produces no new entailments in that sense.
>
> Is it then your contention that schema:domainIncludes does not add any
> new entailments under the schema.org semantics?

Sorry, I misspoke.  I did not mean to be taking a position on that, as I 
have not looked at that in any detail.  The intent of my post was only 
to point out how -- even if there weren't any new entailments -- 
schema:domainIncludes *does* still enable some useful inference for 
error checking purposes.

>
>
>> But it *does* enable another kind of very useful machine-processable
>> inference that is useful in error checking, which I'll describe.
>>
>> In error checking, it is sometimes useful to classify a set of
>> statements into three categories: Passed, Failed or Indeterminate.
>> Passed means that the statements are fine (within the checkable limits
>> anyway): sufficient information has been provided, and it is
>> internally consistent.  Failed means that there is something malformed
>> about them (according to the application's purpose). Indeterminate
>> means that the system does not have enough information to know whether
>> the statements are okay or not: further work might need to be
>> performed, such as manual examination or adding more information
>> (facts) to the system. Hence, it is *useful* to be able to quickly and
>> automatically establish that the statements fall into the Passed or
>> Failed category.
>>
>> 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.
>
> I don't see that the CWA is particularly germane here, except that most
> formalisms that do this sort of checking also utilize some sort of CWA.
> There is notthing wrong with performing this sort of analysis in
> formalisms that do not have any form of CWA.  What does cause problems
> with this sort of analysis is the presence of non-trivial inference.
>>
>> 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).
>
> Sure, but it can be very tricky to determine just what facts to consider
> when making this determination, particularly with the upside-down nature
> of schema:domainIncludes

My assumption in this example is that the application already has a set 
of assertions that it intends to work with, and it wishes to error check 
them.

>>
>> 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.
> The CWA actually works against you here.  Given the following triples,
>
> x ppp y .                       # Triple A
> y rdf:type ddd .                # Triple B
> ppp schema:domainIncludes ccc.  # Triple C
>
> you are determining whether
>
> y rdf:type ccc.                 # Triple E
>
> is entailed, whether its negation is entailed, or neither.  The relevant
> CWA would push these last two together, making it impossible to have a
> three-way determination, which you want.

I don't think that's quite it.  The error check that I described is not 
the same as checking whether NOT(y rdf:type ccc) is entailed.  (Such a 
conclusion could be entailed if there were an owl:disjointWith 
assertion, for example.)  It is checking whether (y rdf:type 
KnownDomain(ppp)).  In other words, the CWA is not being made in testing 
whether (y rdf:type ccc); rather it is being made in computing 
KnownDomain(ppp).

The net effect of this is that the CWA is being used to distinguish 
between cases that would all be considered "unknown" under the OWA.

David

>
>>
>> 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.
>>
>> David
>
> peter
>
>
>
>
>

Received on Monday, 31 March 2014 20:40:22 UTC