Re: Two bugs in the OWL 2 Direct Semantics and the SS&FSS documents

On Montag, 29. März 2010, Boris Motik wrote:
> Hello,
> 
> The change would mean that no ontology can enforce ISNAMED to be true only
>  on named individuals. This *does not* mean that an ontology can entail
>  ISNAMED to be true of an anonymous individuals. Rather, this merely means
>  that, if asked for an anonymous individual, ISNAMED can be concluded to be
>  neither true nor false.
> 
> This, however, is just a technicality. If you don't check entailment of
>  keys, you actually can't ask a question by means of which you would be
>  able to tell the difference. Thus, for most practical intents and
>  purposes, this change would be harmless.

I agree with Boris that his proposal is the most sensible solution to fix the 
problem, so that the specification expresses what its designers and 
implementers have expected it to express all the time.

Here is another informal explanation that may help to see why the suggested 
fix makes sense:

Basically, we want ISNAMED to behave like a new class name for which we have 
assertions of the form

 ClassAssertion( ISNAMED :a )

for all individuals :a in the import closure of the ontology. This is the 
approach taken in most research works on which easy keys are based. It is 
important that every interpretation can assign its own class interpretation to 
this auxiliary "class" ISNAMED. This freedom of interpretation acknowledges 
the possibility of having further named individuals in addition to the ones 
that are given in the ontology, and at the same time it does not lead to any 
unwanted conclusions about such additional named individuals. It merely adds 
some uncertainty and openness, but no new truths.

Now of course we do not want to extend the vocabulary with a class name 
"ISNAMED," yet we want its interpretation to be different among different 
interpretations. But if the "class interpretation" of ISNAMED is not 
determined by the class interpretation function of an interpretation, we must 
add it as another explicit component that constitutes an interpretation. This 
is, in essence, what Boris suggests. I do not see a cleaner and more elegant 
solution.

Of course, the intuitive explanation I tried to give here is largely 
irrelevant for the technical correctness of the proposed change. I still hope 
that it can be a useful perspective for understanding the rationale behind it.

Regards,

Markus

> 
> On 29 Mar 2010, at 22:10, Alan Ruttenberg wrote:
> > On Mon, Mar 29, 2010 at 11:20 AM, Boris Motik
> >
> > <boris.motik@comlab.ox.ac.uk> wrote:
> >> 1. A bug in the OWL 2 Direct Semantics
> >>
> >> Section 2.3 of the Direct Semantics document defines the ISNAMED
> >> function, which is used in the definition of the semantics of easy keys.
> >> Unfortunately, this function has been defined to be true for an element
> >> of the domain *if and only if* it interprets a named individual, whereas
> >> it should be true *if* an element interprets a named individual (leaving
> >> open whether ISNAMED is true for other elements). This makes easy keys
> >> not so easy: as a side-effect of this definition, ISNAMED acts as a
> >> nominal, which has consequences for the computational properties of the
> >> profiles. In particular, ontology entailment (which is the basic
> >> computational problem for OWL 2) becomes NP-hard with keys in OWL 2 EL.
> >>
> >> We can fix the error by the following two steps:
> >> - We need to make ISNAMED a part of an interpretation. Thus, an
> >> interpretation needs to become a tuple of the form I = ( ΔI , ΔD , ⋅ C ,
> >> ⋅ OP , ⋅ DP , ⋅ I , ⋅ DT , ⋅ LT , ⋅ FA , ISNAMED). - We need to weaken
> >> the definition of ISNAMED from iff to if. That is, for each named
> >> individual a, ISNAMED(a^I) must be true (but not the other way around).
> >
> > Wouldn't that mean that there could be a valid OWL ontology where
> > isNamed is true of an anonymous individual?
> >
> > How would such an ontology be expressed in the functional syntax?
> >
> > -Alan
> 


-- 
Markus Krötzsch
Karlsruhe Institute of Technology (KIT), Institute AIFB
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