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Re: How does RDF/OWL formalism relate to meanings?

From: Pat Hayes <phayes@ihmc.us>
Date: Tue, 13 Apr 2004 12:11:30 -0500
Message-Id: <p06001f58bca1c861bd08@[10.0.100.76]>
To: Bijan Parsia <bparsia@isr.umd.edu>
Cc: public-sw-meaning@w3.org

>On Apr 12, 2004, at 12:30 PM, Pat Hayes wrote:
>
>>>On Apr 11, 2004, at 11:04 PM, John Black wrote:
>>>  [snip]
>>>  In the RDF Semantics Recomendation it states:
>>>
>>>  "1.2 URI references, Resources and Literals.
>>>  This document does not take any position on the way that URI references
>>>  may be composed from other expressions, e.g. from relative URIs or
>>>  QNames; the semantics simply assumes that such lexical issues have been
>>>  resolved in some way that is globally coherent, so that a single URI
>>>  reference can be taken to have the same meaning wherever it occurs."
>>>  - http://www.w3.org/TR/rdf-mt/#urisandlit
>>>
>>>  What is the effect of the language, "...so that a single URI
>>>  reference can be taken to have the same meaning wherever it occurs."?
>>>  How important is this assumption to RDF semantics?
>>>
>>>  Upon reflection, that isn't the best wording.
>>
>>  Indeed.
>
>Upon reflection, using whitespace for quoting in emaijl isn't the best idea ;)
>
>>>  Roughly: In the *graph* there are only absolute URIs. There also 
>>>are no contexts, so every node labeled with the same uri is 
>>>equivalent.
>>>
>>>  *Between* graphs, however, URIs can behave quite differently 
>>>(until you merge them).
>>
>>Oh, no, wait a minute. That's very misleading. First, URI's don't behave.
>
>Oy, yes.
>
>But interpretations of distinct graphs need not assign the same 
>domain entity to the same URI.

Distinct interpretations need not assign the same entity, right. But 
an interpretation is of a vocabulary, not of a graph. So its 
misleading to speak of interpretations of my graph vs. of your graph. 
The distinctness of the graphs, and of the interpretations, are 
orthogonal.  I can apply your interpretation to my graph, and vice 
versa. The ambiguity arises from the multiple interpretations (which 
we might as well think of as applied to the entire vocabulary of all 
URIs) not from the multiplicity of the graphs.

>So, unless you merge the graphs, the URIs can have different meanings. Right?

No.

Well, yes and no. They can have multiple meanings whether you merge 
the graphs or not.

The trouble is., the phrase "same meaning" isnt precise enough here. 
For URis (names, logical constants, identifiers, whatever) there are 
two MT senses of "meaning". One is the actual intended referent in 
the actual real world, assuming you believe in such a thing and there 
actually is one.  (In this sense, the TAG wants it to be the case 
that URIs have only one meaning, but I think its fine if they have 
more than one, ie are ambiguous as names. )  Another sense of 
"meaning" is the referent of the URI *in a given interpretation*, or 
equivalently a function from interpretations to things.  Given a 
graph, this second sense of meaning picks out a set of possible 
referents which gets smaller as you add more information to the 
graph.  However, note that in that second sense - the only sense in 
which a URI might be said to be ambiguous - its just as ambiguous for 
you as it is for me. That is, the ambiguity here isn't that you have 
one referent and I have a different referent: its that both of us 
don't know what the referent is (assuming that is that we have access 
to the same information: if you have access to more information than 
I have then you might be able to pin down the referent to a smaller 
set of possibilities than I can - your meaning in this second sense 
might be tighter than mine.)

>>  Second, if they did behave, then they ought to behave the same 
>>independently of any merging, since merging graphs does not alter 
>>URIref meanings.
>
>Really? Huh.

Again, need to say this more carefully. Merging graphs can certainly 
restrict the set of satisfying interpretations, so can make the set 
of possible referents smaller. In fact if A is the set of possible 
referents of a node given a graph G and B is the set given another 
graph H, then the set of possibilities given the merge off G and H is 
a subset of the intersection of A and B.  The point I intended to 
make by the above was that if you think in the first way, so that the 
'meaning' is a single referent, then merging can't change that. This 
is really a special case of monotonicity, in fact.

>There seems *some* sense in which it does, as mergine graphs can 
>alter the set of axioms in effect (talking about OWL, now).

Right: see above.

>>It is important that a single URI is the same no matter what graph 
>>it occurs in. URIreferences scope across the entire Web, so a given 
>>URIref in your graph and in my graph really are the same URIref.
>
>I don't believe that.

Well, get used to it. This is vital to the SWeb. URIs are the same 
everywhere. Your graph might have more stuff in it, so the set of its 
satisfying interpretations may be smaller than mine: but the actual 
URI, the syntactic 'name' (sorry, Dan, if you are reading this) is 
the same in my graph as in yours. And if I get hold of your graph 
then my grip on what that piece of naming syntax is supposed to 
denote is exactly as tight as yours.

>>If they weren't, there really would be no difference at all between 
>>URIrefs and blank nodes, and RDF graphs would be essentially 
>>all-blank graphs.
>
>Sure there is: Behavior under merging.

But that behavior is only the way it is BECAUSE URIrefs are global 
identifiers which are the same everywhere. If they weren't, we would 
have defined merging differently.

>>>I'd say it's pretty important :)
>>>
>>>  Note that URIs in literals (e.g., in literals of datatype 
>>>xsd:anyURI) are exempt from this merging. So the above text isn't 
>>>quite right if you try to read it in full generality.
>>
>>No, it is right and they aren't exempt.  A typed literal in RDF 
>>consists of a URIref denoting the datatype  and a STRING which is 
>>the lexical form of the datatype.
>
>What, no values?

Right, no values. You can't put most values into syntax. Take 
integers, for example. The literal

"17"^^<xsd:integer>

actually contains a string which is an encoding of a numeral, not a 
number. The value is a natural number (called in English 
"seventeen"), but you can't send a natural number over a network. The 
literals denote the values, but they don't exhibit them in their 
syntax (usually).

>>So in your example, the only actual URIref in the literal is 
>>http://www.w3.org/2001/XMLSchema#anyURI which is a genuine 
>>first-class URIref and has the same meaning there as it does 
>>everywhere else, and indeed might also occur in non-literal 
>>triples, eg
>>
>><http://www.w3.org/2001/XMLSchema#anyURI>  rdf:type rdfs:Datatype .
>
>And others!
>
>>The other part of the literal is a character string which indicates 
>>the lexical form of (in this case) a URI, but it is not itself an 
>>actual URI. The URI you are talking about is what this typed 
>>literal DENOTES, ie the datatype value of the lexical form under 
>>the lexical-to-value mapping (in this case, from strings to URIs) ; 
>>but it doesn't, strictly speaking, occur anywhere in the RDF syntax.
>
>Ah, right. For some reason I got stuck in my head that literals are 
>self denoting.

Plain literals are, providing you ignore those bloody lang tags.

Pat


>
>Cheers,
>Bijan Parsia.


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Received on Tuesday, 13 April 2004 13:17:54 GMT

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