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

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 semantics?

> 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 
> 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 .
y rdf:type ddd .
ppp schema:domainIncludes ccc.

you are determining whether

y rdf:type ccc.

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.

> 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


Received on Monday, 31 March 2014 16:00:19 UTC