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Re: Unique denotation assumption

From: Pat Hayes <phayes@ihmc.us>
Date: Wed, 11 Sep 2013 20:15:04 -0700
Cc: www-archive <www-archive@w3.org>
Message-Id: <F4946CC0-FED3-4183-82D6-DB4C498081D2@ihmc.us>
To: David Booth <david@dbooth.org>

On Sep 11, 2013, at 6:14 PM, David Booth wrote:

> hi Pat,
> 
> Since the RDF WG does not have a public discussion list to which non-members can post, I'm copying the public www-archive list.  I want to propose a couple of changes to the RDF specs, and thought it might save the WG and others time if I first discuss them with you (and anyone else you think would be interested).  One of them is the following.
> 
> In https://dvcs.w3.org/hg/rdf/raw-file/default/rdf-concepts/index.html
> I see this statement:
> 
>  "IRIs have global scope: Two different appearances of an IRI
>  denote the same resource."
> 
> This is wrong

It is a foundational assumption of RDF. Without this assumption, graph merging would never be a valid operation, and no RDF engines could combine informationfrom different sources to draw conclusions. 

> , because an IRI can and often does denote different resources in different RDF interpretations.

That is irrelevant to the point being made in the sentence you cite above. No interpretation allows two occurrences of a single IRI to denote different things. 

>  And this, in practice, means that an IRI often denotes different resources in different *graphs*

No, it does not. What is true, of course, is that the sets of interpretations which satisfy the two graphs will be different, and each will likely be different from the set of interpretations satisfying both of them (their union.) But that does not imply that IRIs in different graphs denote differently. 

> , because any graph has a set of satisfying interpretations, and different graphs may have different sets of satisfying interpretations.

Yes, but that does not imply what you seem to think it implies. 

>  For example, suppose graphs g1 and g2 have sets of satisfying interpretations s1 and s2, respectively, and those sets may be disjoint.  Then colloquially (and technically) we can say that an IRI may map to one resource in g1 (i.e., in some interpretation in s1) and a different resource in g2 (i.e., in some interpretation in s2).

No, that would not be a correct way to express this condition, even colloquially. What you are describing is two graphs which contradict each other in some way. Which is impossible  in RDF but much easier to arrange in RDFS or OWL or other more expressive languages, but in any case it is often only possible to detect the contradiction when we presume that IRIs denote uniformly across graphs. Take this example, using some rdfs:

G1:  
ex:a ex:p "23"^^xsd:number .

G2:
ex:p rdfs:range xsd:string .

Each is consistent (has satisfying interpretations) but together they are inconsistent (recognizing XSD). Why? Because if ex:p has range xsd:string, then the first triple in G1 implies that a nuber must be an XSD string, and XSD says these are disjoint. But notice, this line of reasoning assumes that the ex:p in the G1 is the same ex:p as in G2. If it wasn't  if the same IRI in two different graphs could denote different things  then there would be no inconsistency here, because G2 might be talking about a different thing than the ex:p that G1 is talking about. 

> 
> This requires thinking about graphs in terms of sets of satisfying interpretations -- an important and valid perspective -- rather than assuming that one looks at them only through the lens of a single interpretation.

Of course we think of graphs in terms of sets of satisfying interpretations. That does not imply that different occurrences of an IRI can denote differently.

> 
> In short, I think the above statement needs to be qualified somehow, such as:
> 
>  "IRIs are intended to have global scope: Two different
>  appearances of an IRI are intended to denote the same resource.
>  (But see RDF Semantics for caveats regarding different RDF
>  interpretations.)"

The semantics document has no such "caveats". 
> 
> And then we would have to add something to the RDF Semantics document to explain how an IRI can denote different things in different interpretations.

Of course IRIs denote different things in different interpretations. That is what interpretations are all about: each interpretation is one way to construe what IRIs mean, one mapping from IRIs to denoted things. But each one of them construes each IRI in a particular way. It does not construe one occurrence of a given IRI in one way, and a different occurrence of the same IRI in a different way. That condition  we might call it a 'split reference'  is not possible in any interpretation. In fact, it is explciitly ruled out by the very construction of interpretations, which are defined as mappings from IRIs to referents. Not from *occurrences* of IRIs to referents, notice. 

> 
> Does this make sense to you?

Clearly not; but you knew this, surely, from our earlier extended discussions on this topic.

>  Comments?

See above. 

Pat

> 
> David
> 

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Received on Thursday, 12 September 2013 03:15:29 UTC

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