Re: owl:sameAs - Is it used in a right way?

On Mar 22, 2013, at 10:30 PM, David Booth wrote:

> On 03/21/2013 01:02 PM, Pat Hayes wrote:
>> On Mar 20, 2013, at 9:58 PM, David Booth wrote:
>>> On 03/20/2013 12:04 AM, Pat Hayes wrote:
>>>> On Mar 18, 2013, at 4:04 PM, David Booth wrote:
>>>>> On 03/17/2013 10:02 PM, Pat Hayes wrote:
>>>>>> On Mar 16, 2013, at 11:26 PM, David Booth wrote:
>>>>> [ . . . ]
>>>>> But presumably that passage from Section 1.2 means ". . .
> >>>> [the semantics simply assumes that ... a single URI reference
> >>>> can be taken to have the same meaning
> >>>> whenever it occurs] _in the *given* graph, i.e., the graph
>>>>> whose semantics are being determined_",
>>>> 
>>>> No, it means wherever they occur, period. If they occur in
>>>> several graphs, they all refer in the same way in all of them.
>>> 
>>> Absolutely not.  That is only true for *one* interpretation.
>> 
>> Absolutely yes. It is true for all interpretations. There is no
>> interpretation which allows a single URI to refer in different ways
>> when it occurs in different graphs.
> 
> Uh-oh, there's that single-interpretation assumption creeping in again!

No assumption is creeping anywhere in that statement. I said, for ALL interpretations. 

>  While it is true that there exists no *single* interpretation that allows a single URI to refer in different ways when it occurs in different graphs

There exists no interpretation which ... No need to say or emphasise "single". 

> , surely you would agree that under standard RDF Semantics:
> 
>  There exist interpretations I1 and I2, RDF graphs G1 and G2,
>  URI U and resources R1 and R2, such that I1 maps U to R1,
>  I2 maps U to R2, and R1 != R2.

Of course.

> Therefore, under standard RDF Semantics:
> 
>  1. A URI can map to *different* resources in *different* graphs.
>  (Proof sketch: Use I1 for one graph and I2 for the other.)

No, and your proof is faulty. You don't get to use an interpretation for one graph and a different interpretation for the other. Each interpretation is a mapping *on names*, not on graphs. GIven such an mapping on names, the truth or falsity of all graphs is determined. 

What does it mean to "use" I1 on G1 and "use" I2 on G2? Each of I1 and I2 apply to all the names in both G1 and G2. The "combination" you have sketched is not an interpretation mapping, so (a) what is it? and (b) what relevance does it have to what we are talking about, which is interpreting RDF graphs? 

Here's the corrected version: 

1. Lemma. A URI maps to the same thing, no matter what graph it occurs in. (Proof: Let I be an interpretation mapping and U a URI. Then I maps U to I(U). The previous sentence did not mention graphs, so it applies regardless of what graphs contain U. But I was arbitrary, so this is true of any interpretation. QED.)

>  2. A URI can map to *different* resources.
>  (Proof sketch: Use different interpretations, I1 and I2.)

In different interpretations, yes, of course. 

> Some may claim that this

What is "this" ?

> is a misuse of the RDF Semantics -- that there really is only one "correct" interpretation, even though we may not know which one it is.  (This is the single-interpretation assumption.)  But the RDF Semantics makes no such requirement, and to my mind that is part of its genius, because the allowance of multiple interpretations is valuable!  It lets us better account for the real world use of RDF -- **under standard RDF Semantics** -- because in the real world, RDF authors *do* make different assumptions in their interpretations of URIs, and different RDF consumers *do* apply different interpretations to the URIs they encounter.

> I have separately tried to point out how the existing RDF Semantics spec already supports a poor person's notion of context *because* of its allowance of multiple interpretations:
> http://lists.w3.org/Archives/Public/public-semweb-lifesci/2013Mar/0099.html

But your argument there is faulty, because the presence of multiple interpretations does not, by itself, provide any notion of context, poor or otherwise. 

> The purpose of a context is to enable the same RDF graph to have different truth-values in different contexts.

Actually, more basically, it is to enable a single URi to refer to different things in different contexts. Which then has the graph consequence that you mention. 

>  But this is exactly what an interpretation does!  

No, that is not what an interpretation does. An RDF interpretation maps each URI into a single referent (and each graph to a single truth-value.). It does not provide for one URi to have different meanings in different contexts, because it does not provide any contexts to pur URIs into. To do that, it would have to be a mapping from (URIs x contexts) to referents. 

> So if you think of an RDF interpretation as a context -- which IMO is quite a natural way to think of it

I am afraid that if this seems natural to you, then you really have not understood the basic idea of model-theoretic semantics. (Ask yourself: if interpretations are contexts, how does one provide a semantics for an actual context logic, such as ICL or Cycl, which has names for contexts in the syntax of the language? And if interpretations are contexts, then all logics ever invented have been context logics, so why did context logicians feel that they had any need to invent them again? And what did Guha get his doctorate for, if all the work he did was already somehow inside the standard Tarski model theory?) 

> -- then different RDF graphs can *already* be interpreted in different contexts (i.e., according to different RDF interpretations) under the *existing* RDF Semantics, because as we have laboriously agreed, **the existing RDF Semantics allows different interpretations to be applied to different RDF graphs**.

I hope I did not agree to that as stated. The semantics allows for different interpretations, and it defines the truth of a graph in an interpretation. Each interpretation determines the truth-value of *all* graphs. The semantics does not mention, and does not provide any way to make sense of the idea of, applying one interpretation to one graph and a different interpretation to another graph. That idea is a pure figment of your imagination. 

> [Actually, to be slightly more technical, in this approach to contexts it would be better to view a context as a *set* of interpretations, rather than a single interpretation, because it is still useful to talk about the set of satisfying interpretations for an RDF graph, subject to a particular context.  But that's an unimportant detail at the moment.]
> 
> Indeed, people *already* use RDF graphs in this way: intentionally keeping graphs separate if they come from different perspectives, sources, provenance, etc., *because* the graphs may cause inconsistencies or lead to incorrect conclusions if merged injudiciously.

That is true, but...

>  Knowingly or not, different interpretations are being used for different graphs.

...that does not follow. Consider: if the URIs referred differently in the various graphs, then these graphs would *not* cause inconsistencies if taken together. The inconsistencies arise precisely *because* we all assume that a given URI denotes the same thing in every graph in which it occurs, and that interpretations apply across graphs. 

> A simple example is Ian Davis's famous toucan-versus-its-web-page example,
> http://blog.iandavis.com/2010/11/04/is-303-really-necessary/
> in which the same URI "ambiguously" denotes both a toucan and the web page describing that toucan.  One RDF graph, Gt, may be written under the assumption that the URI denotes the toucan.  Another graph, Gp, may be written under the assumption that the URI denotes the toucan's web page.  Gt may work perfectly well in an application that merely categorizes different animal species -- *unambiguously* interpreting the URI as denoting the toucan.  And Gp may work perfectly well in an application that merely lists web page authors -- *unambiguously* interpreting the URI as denoting the toucan's web page.  In fact, even the merge of Gt and Gp may work perfectly well in both applications, provided the RDF authors have not asserted that toucans are disjoint from web pages!

This is called punning, AKA overloading. As you point out, it works up to a point. But this is not context reasoning. In fact, it is might be described as un-context reasoning: it is what happens when you mush what should be distinct contexts into a language which does not have a context mechanism to distinguish them. If this were written in a real context logic, then you would have explicit contexts for the two distinct meanings. 

> Applications that consume RDF and faithfully follow the RDF Semantics are free to choose their own interpretations, and this is A Good Thing.
> 
> On the other hand, an application that needs to distinguish between web pages and animal species will find this toucan/webpage URI hopelessly ambiguous, and will not be at all happy with the merge of Gt and Gp. This is why I have been pointing out (in other conversations) that ambiguity is *relative* to the application: a URI may be unambiguous to some applications, but ambiguous to others.
> 
> But although the existing RDF Semantics does support this simple "poor person's" notion of context-as-interpretation (or context-as-set-of-interpretations), it does not support other basic features that one would expect in a context-aware semantics.  Most notably, it does not support the ability to retain contextual differences when RDF graphs are merged.  To account for that and a few other basic operations, the RDF Semantics would indeed have to be extended, as you and a few others have proposed.
> 
> [ . . . ]
>>>> The semantic rules simply specify when a graph (any graph) is
>>>> true in an interpretation (any interpretation). But
>>>> interpretations are not defined "on" graphs: they are mappings
>>>> from *names* to things. That does not mention graphs at all. So
>>>> to then start talking about one graph in one interpretation and
>>>> another graph in another interpretation simply misses the point.
>>>> The fact that there are many possible interpretations is a
>>>> reflection of the fact that we typically are in a state of doubt
>>>> about what the names (URIs) actually refer to.
>>> 
>>> That sounds dangerously close to falling into the trap of assuming
>>> that there really is only one, global, correct interpretation.  And
>>> it is *my* interpretation, of course.  ;)
>> 
>> It is not anyone's interpretation: it is the fact of the matter. Of
>> course, we don't have access to the facts, only our representations
>> of them, which allow many interpretations.
> 
> I don't see how this "fact of the matter" has any relevance

I probably shouldn't have mentioned it, as it seems to have been more confusing than enlightening. (It is the standard way to understand model theory when discussing mathematics, eg people talk about "standard arithmetic", meaning the single "correct" way to interpret formal arithmetics.)

Pat

 
> , since: (a) the RDF Semantics says nothing about it; and (b) it is an application's own business what interpretations it chooses to use.  If that application causes some harm by applying the wrong interpretation, then the owner may be liable, but that is an entirely separate issue from the question of compliance with the RDF Semantics.
> 
> David
> 
> 
> 
> 

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Received on Saturday, 23 March 2013 04:50:09 UTC