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?
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
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
peter
