Re: POWDER formal semantics 4.3 comments

I'm diving a bit deeper into the relation between RDF formal semantics  
[1] and POWDER formal semantics [2], and have found another glitch.

POWDER says:

           o uuu is in the domain of I, with I(uuu)=x

Clearly uuu is meant to be an IRI. But RDF semantics says that the  
"domain" of an interpretation I is a set of resources (somewhat  
confusingly, since I is also used as a function that has a domain that  
is syntactic). I think you mean for uuu to belong to V, the  
"vocabulary" of I, which is the domain not of I but of IS:

"A set of names is referred to as a vocabulary [V]."  ... "4. A  
mapping IS from URI references in V into (IR union IP)" ... "if E is a  
URI reference in V then I(E) = IS(E)"

I couldn't find any particular restrictions on what V might be; it  
could be empty, or the set of IRIs, or the set of IRIs occurring in  
the graph, or anything else. I would guess that in applying an  
interpretation to a graph, the name (IRI) set is meant to at least  
contain the vocabulary of the graph (the IRIs) occurring in it, but it  
could be limited to it.

Now there are two problems with this. First, you want to talk about  
IRIs, not URIrefs, right? That is, if the RDF graph contains the  
relative URIref "a/b", you would prefer to match against the fully  
resolved IRI, not the URIref, since otherwise the truth of a POWDER  
graph would depend on choice of base IRI, which makes no sense. So you  
need to have a story that accounts for the base URI (or other  
resolution mechanism), or else arranges for all IRIs to be fully  
resolved by the time they get to this point. Perhaps this is already  
taken care of, and I'm just missing it.

Second, the restriction of POWDER formal semantics to the IRIs that  
are in the vocabulary of the interpretation (= domain of IS = V) will  
only sometimes agree with the informal semantics that you are trying  
to capture. Suppose a graph contains assertions that the resources  
named by a/x, a/y, and a/z (imagine now these are IRIs) are green. If  
these are the only IRIs of the form a/* occurring in V, one could  
conclude, according to your semantics, that all the resources in the  
group defined by IRI pattern a/* are green. But there might be another  
resource, a/w, that is not green, but just happens to not be mentioned  
in this particular graph. The formal semantics would agree with the  
informal semantics only in the case that all resources with IRIs  
matching a/* occur in the graph.

On the other hand, model theoretic semantics (for either RDF or OWL- 
DL) might handle this well, since entailment is quantified over all  
possible models, and at least one of these will include information  
about a/w. But the fact that some of your interpretations are wrong  
means that you will get fewer entailments than you might otherwise  
like. It might be worth the effort some time to restrict  
interpretations further.

Still trying to get a grip on this.



Received on Thursday, 20 November 2008 17:06:54 UTC