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Re: ISSUE-69 (punning): REPORTED: punning is incompatible with OWL Full

From: Bijan Parsia <bparsia@cs.man.ac.uk>
Date: Wed, 21 Nov 2007 11:14:48 +0000
Message-Id: <A48A9C7B-89D6-4CB1-93FE-8CA5EDAA12D7@cs.man.ac.uk>
To: OWL Working Group WG <public-owl-wg@w3.org>

On 20 Nov 2007, at 15:08, OWL Working Group Issue Tracker wrote:

> ISSUE-69 (punning): REPORTED: punning is incompatible with OWL Full
>
> http://www.w3.org/2007/OWL/tracker/issues/
>
> Raised by: Jeremy Carroll
> On product:

I don't believe this is technically correct. At the least, a clear  
notion of incompatibility must be presented.

> OWL Full 1.0 allows any URI to function in the various roles of  
> individual, data property URI, object property URI, class etc. etc.
>
> Under OWL Full semantics this is not punning but identity.

This is not a technical difference, but a presentational one. It is  
perfectly possible to use the OWL Full EXT semantics to specify  
punning (or, as it is sometimes know, "contextual" semantics).  
Similarly, there are things which under a robust notion of "identity"  
OWL Full fails to achieve. The most obvious one is that in a  
traditional model theory, predicates are interpreted as *sets* (of  
tuples). In RDFS/OWL Full they are interpreted as *individuals* which  
are *related* to sets.

In fact, I believe that by suitable modification of the  
interpretation function, we can get either punning or hilog  
entailments out of the same structures.

> The proposed semantics for punning in the member submission is  
> *weaker*,

Weaker than OWL Full semantics, yes. As it true already in OWL 1.0  
(i.e., some graphs are OWL DL consistent but OWL Full inconsistent).  
Indeed, a similar situation exists with RDFS (i.e., domain reasoning  
is weaker, for the same graphs, than in OWL DL).

> so that the member submission either requires:
> - a non backward compatible change to OWL Full semantics

But a largely harmless one, in that no reasonably complete OWL  
reasoner will break (and certainly no editors). Some very weak  
reasoners will break slightly, but in ways that are recoverable by a  
rule extension (which is, indeed, how they are realized, typically).

> - or a weakening of the relationship between OWL DL and OWL Full,  
> so that DL is a fragment of OWL.

It is very hard to see that the addition of punning is *anything* but  
a *strengthening* of the relationship between OWL DL and OWL Full.  
Here's a presentation that makes that clear.

The intuition: The more two languages share 1) legal formulaes and 2)  
entailments, the closer they are.

For example, in OWL DL, there are *many* RDF graphs that are not  
legal. For example:

	C rdf:type D.
	C subClassOf D.

Roughly the well formed formulae of OWL DL (WFF(DL)) are a subset of  
those of OWL FULL (WFF(Full))
	WFF(DL) strictsubset WFF(FULL)

Note that this has been *IN PRACTICE* a huge problem. People write  
illegal OWL DL graphs and want to use them with OWL DL tools. Hence  
the whole "repair" business. Pellet, in fact, will often *more or  
less silently* repair ontologies.

If we add punning (alone) to OWL DL, we end up with a strictly larger  
subset of WFF(Full) being legal, i.e.,
	WFF(DL) stirctsubset WFF(DL+Puns) strictsubset WFF(Full)

Thus, in this respect, DL+Puns has a stronger relationship to Full.

So what of entailments? Well, the entailments of DL+puns (E(DL+puns)  
*also* a strict subset of the entailments of Full (E(DL+Puns).  
Indeed, there are many cases where the entailments coincide (i.e., as  
Boris shows in his paper, if you don't have equality (or perhaps even  
equality between classes and properties) then punning and full  
semantics are *the same8).

Thus,
	E(DL) strictsubset E(DL+Puns) strictsubset E(Full)

Thus, unsorted grammar plus contextual semantics makes DL a strictly  
larger fragment of  OWL Full, thus better aligns them, i.e.,  
strengthens their relationship.

(And really that's what "punning" is: unsorted user vocabulary plus  
contextual semantics. "Punning" is just a convenient way to think  
about and even implement it. Nothing deeper.)

Note that we added punning to Pellet way back and, thus far, have  
received no complaints about the missing equality to equivalence  
entailments. I can imagine them coming via a general abuse of sameAs  
for mapping, but I'm very much inclined not to support that use case  
(I argue strongly against it as a practice). In any case, *that* use  
case (in practice) typically only asserted (or near asserted)  
equalities between atomics (e.g., people would be very surprised by  
equivilences derived by equalities based on case reasoning).

Cheers,
Bijan.
Received on Wednesday, 21 November 2007 11:13:27 GMT

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