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Re: ISSUE-3: REPORTED: Lack of anonymous individuals

From: Carsten Lutz <clu@tcs.inf.tu-dresden.de>
Date: Thu, 08 Nov 2007 13:29:25 +0100 (CET)
To: Boris Motik <boris.motik@comlab.ox.ac.uk>
Cc: public-owl-wg@w3.org
Message-id: <Pine.LNX.4.64.0711081308200.20460@frege.inf.tu-dresden.de>

Hi Boris,

I see your point in favour of skolem constants and cannot really comment
on it. If your assumption is correct that this is the main use of
anonymous individuals, skolem constants are fine. Whether the
assumption is correct, I have no idea.

The point that I was raising in the TeleCon was that *true* anonymous
individuals (not the skolem ones) are of course closely connected to
the universal property, i.e., a special property that is simply
interpreted as the total relation. To say that there is an anonymous
object "a" that is a C, you could say that the top class (how is this
called in OWL? Is it available in OWL? If not, add it :) implies
(objectSomeValuesFrom (uprop C)), where uprop is the universal property.
It can easily be modified to state the existence of multiple
anonymous individuals that are related in a tree-shaped way. You can
also say more complicated things with the universal property such as
"if every A is a B, then a is a C".

In my opinion, the universal property is quite useful, and we should
consider adding it. This may be a separate issue, but there is a close
relation. Actually, we could think of adding the universal property
and interpreting the anonymous individuals as skolem constants, as you
propose. This means that, if really needed, true anonymous individuals
can still be recovered via the universal property. The restriction to
tree-shaped interconnections is then automatic. And we don't introduce
conjunctive queries to ontology entailment.

greetings,

 	Carsten

PS: If we decide to admit the universal property, we of course have to
     be a bit careful. In particular, it may be wise not to admit it in
     role inclusions, and not to admit it in number restrictions.



On Wed, 7 Nov 2007, Boris Motik wrote:
>
>
> Hello,
>
> The OWL 1.1 Member Submission does not contain anonymous individuals for the reasons I explain below. These reasons are related to
> ISSUE-46: Unnamed Individual Restrictions (http://www.w3.org/2007/OWL/tracker/issues/46). It might make sense to discuss both issues
> together.
>
> In short, we did not include the anonymous individuals into the Member Submission because they significantly affect computational
> aspects of the logic (explained under item 1 below). Furthermore, anonymous individuals are usually used in practice with a weaker
> semantics (explained under item 2 below). Therefore, we did not introduce anonymous individuals in the Member Submission and wanted
> to discuss this in the working group.
>
>
>
> 1. Why can nontree-like "true" anonymous individuals be dangerous?
>
> Nontree-like "true" anonymous individuals in the ABox cause undecidability of ontology entailment, which is the basic inference
> problem for OWL. An ABox containing anonymous individuals can actually be understood as a conjunctive query. It is well known that
> answering conjunctive queries over SHOIQ TBoxes is undecidable if you allow the query to contain inequalities. Details can be found
> in the following paper, but I can give further explanation if needed.
>
>    Diego Calvanese, Giuseppe De Giacomo, and Maurizio Lenzerini:
>    Conjunctive query containment and answering under description logics constraints,
>    ACM Trans. on Computational Logic, 2007. To appear.
>
> Finally, DifferentIndividuals ABox assertions are actually inequalities. To summarize, if you allow nontree-like anonymous
> individuals in DifferentIndividuals ABox assertions, you easily get undecidability of the basic reasoning problem.
>
>
> Even if you were to forbid arbitrary anonymous individuals in the DifferentIndividuals assertions, ontology entailment would still
> require answering conjunctive queries over DL TBoxes. Currently, we only know that this problem is decidable for SHIQ; however, it
> is not clear whether this is the case for SHOIQ as well.
>
>
> The bottom line is that nontree-like "true" anonymous individuals are computationally hard, so it might be prudent to avoid them.
>
>
>
> 2. We could interpret anonymous individuals as Skolem constants
>
> In practice, the semantics of anonymous individuals as true existentially quantified variables is rarely needed. Usually, anonymous
> individuals are used just as a convenience, saving the ontology modeler from the trouble of inventing a name for the individual. I
> am not aware of any practical system (OWL or RDF) that implements the semantics of anonymous individuals as true existentially
> quantified variables.
>
> Therefore, rather than introducing "true" anonymous individuals, we might simply interpret them as Skolem constants. In this case,
> we do not need the restriction to tree-like connections, and we could indeed process a larger fragment of RDF data.
>
> Here is a concrete proposal how to reflect this in the specification documents:
>
> - The structural specification would be changed to imbue the Individual class with an "anonymous" flag. This might be useful for the
> presentation of an ontology.
>
> - The semantics document would make no special provisions for the anonymous individuals. Thus, individuals with the "anonymous" flag
> set would be interpreted as all other individuals.
>
> - The mappings to the XML and RDF syntaxes would be extended to update the "anonymous" flag correctly during parsing.
>
> - The semantics of ontology entailment would not change.
>
>
>
> Regards,
>
> 	Boris
>
>
>

--
*      Carsten Lutz, Institut f"ur Theoretische Informatik, TU Dresden       *
*     Office phone:++49 351 46339171   mailto:lutz@tcs.inf.tu-dresden.de     *
Received on Thursday, 8 November 2007 12:29:53 GMT

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