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Re: Requiring semantic extensions to be AZ-proper? (was: Re: Monotonicity of semantic extensions)

From: Pat Hayes <phayes@ihmc.us>
Date: Wed, 12 Sep 2012 23:09:35 -0500
Cc: Antoine Zimmermann <antoine.zimmermann@emse.fr>, public-rdf-wg@w3.org
Message-Id: <971FE59A-4BAD-4FDC-8DD5-76C291511326@ihmc.us>
To: Richard Cyganiak <richard@cyganiak.de>

On Sep 12, 2012, at 3:04 PM, Richard Cyganiak wrote:

> Antoine,
> 
> On 12 Sep 2012, at 18:47, Antoine Zimmermann wrote:
>> I don't know if the phrase "proper semantic extension" is standard, but I guess it maps to something defined by logicians.
>> 
>> What I consider a "proper" semantic extension X of an entailment regime Y has to satisfy the following property:
>> 
>> "For any dataset D1 and D2, if D1 X-entails D2, then D1 Y-entails D2."
> 
> Okay, so let's define some working terminology and call that “AZ-proper”.

That was part of the original idea. We never defined "semantic extension" formally, but it was supposed to be the kind of relationship that RDFS has to RDF and OWL-Full has to RDFS and OWL-DL has to RDF. The basic idea (originally) was that Y is an extension of X when every interpretation of Y is an X-interpretation with some additional constraints on the vocabulary that Y treats as "special". You can see this pattern in how RDFS-interpretations are defined in terms of RDF interpretations, etc.. But then we had to allow for things like the OWL-DL case where the Y actually prohibits some X-legal combinations, and also where it treats some of the X vocabulary as being outside the Y interpretation rules altogether. Which is why the 'general monotonicity lemma' seems, as Antoine notes, to be trying to do several things at once. 

When OWL (well, OWL-DL) came along, the whole picture of how a 'higher' notation related to its RDF embedding got a lot more complicated. I now think that we maybe should simply give up trying to have a single general story to cover all the ways that someone might want to extend RDF, and just admit that ther are some 'proper' ways but that 'improper' ways will happen as well.

> 
> <snip detailed explanation of “AZ-proper” semantic extensions>
> 
> I get this now. Thanks, it was very helpful.
> 
>>> I can't quite figure out what these conditions are just from reading
>>> RDF Semantics. The “general monotonicity lemma” [2] seems relevant,
>>> but is phrased as a result of something being a semantic extension,
>>> rather than as a condition on semantic extensions.
>> 
>> Well, the lemma, which I was not aware of, seems to say that the semantic extensions defined by RDF semantics are satisfying the property that I mentioned (modulo the use of RDF graphs instead of datasets).
> 
> Okay, right.

Yup, right.

> 
>> But it does not define in general a condition on semantic extensions.
>> 
>> I don't think RDF Semantics 1.0 specifies what's a "proper" semantic extension and does not require that any future extension must be monotonic.
> 
> Well, read the second-to-last paragraph here:
> http://www.w3.org/TR/rdf-mt/#intro
> 
> And this:
> http://www.w3.org/TR/rdf-mt/#vocabulary_entail
> 
> And this:
> http://www.w3.org/TR/rdf-mt/#MonSemExt
> 
> I've read all that stuff multiple times, and am still muddled on what it tries to do. But my impression is that it attempts to define a clean extension mechanism for the semantics, where new semantic extensions can be defined and associated with new vocabulary terms, and with scope beyond those entailment regimes defined in the spec itself.

Exactly.

> So, there could have been FOAF-entailment and SKOS-entailment and so on (perhaps defined simply as: In FOAF-entailment, the triples in http://xmlns.com/foaf/spec/index.rdf are considered axiomatic). Maybe I'm reading too much into this?

No, that is exactly right. But the complexities of handling OWL-DL in RDF (which were **way** more complicated and controversial than anything in RDF itself), and which were going on in the OWL WG exactly when the RDF WG was writing the 2004 specs, somewhat shook my confidence in making this whole idea normative. So in the end, it was left both loosely defined and informative, as we really could not see where the whole idea was likely to go.

> 
>> And even though it did say so about extensions of RDF semantics, it would not apply to the semantic of dataset, which does not deal with a set of triples alone.
> 
> But the distinction between “normal” interpretations and “dataset” interpretations could easily be removed, so that every interpretation can interpret RDF terms, RDF triples, RDF graphs and RDF datasets, no? This seems very tempting to me because it would make everything nicely uniform. (I said earlier in the thread that this is probably just an editorial issue.)

I agree this would be very desirable. In fact, being able to do this easily (trivially?) should be a constraint on any plausible semantics for datasets, I suggest. A semantics for datasets that makes them very different from graphs would seem inherently implausible.

> 
>>> By the way, do we agree that RDF Semantics should be very clear and
>>> specific about what it means to define semantic extensions to the
>>> various entailment regimes? I think making that normatively crystal
>>> clear is part of why that spec exists. And in fact, one way how one
>>> can conform to RDF Semantics is by defining a “conforming semantic
>>> extension of XYZ-entailment”, IMO.
>> 
>> Why not, but first we have to agree that we want to prescribe extensions that do not extend monotonically (I want to avoid the phrase "non-monotonic extension" which can have a different meaning).

I agree, lets be ever so careful with terminology here.

Regarding monotonicity or not, let me suggest that we don't exactly proscribe, but use as a heuristic that if a proposal produces nonmonotonic extensions, then this might be a good reason to check it out carefully. KInd of a warning light. 

>> Perhaps there are some cases where it makes sense to do so (e.g., define an extension for working on closed databases).
> 
> Well, we can't stop anyone from doing that, it would just not be an extension that conforms to the requirements of RDF Semantics.
> 
>> Personnaly, I'm in favour of restricting all normative extensions to be monotonical extension.
> 
> I've heard that it's possible to cleanly combine multiple such extensions

Not in general. Very simple ones, maybe. But don't rely on it. Combining conditions on interpretations can have strange effects.

> , especially if the new entailments are “triggered” by the use of vocabulary terms that are specific to the extension. That sounds like a pretty good argument in favour of “AZ-properness” to me.
> 
> I think Pat also said that he'd like to shuffle things around in the RDF Semantics document to make the existing entailment regimes work that way, that is, RDFS-entailment would be “triggered” by the use of a term in the RDFS namespace. That kind of makes sense to me.

What I want to do, if possible, is to make precise what is currently left kind of implicit, which is that using a term from RDFS or OWL "automatically" brings along the relevant fragment of RDFS or OWL meaning. RIght now people use, for example, owl:sameAs in RDF and clearly intend this to mean (something closely related to) what the OWL specs define owl:sameAs to mean, even though they still say they are using RDF rather then OWL. I would like to make this idea more precise than we do right now. But lets leave that issue for now, as we probably won't get that done in this WG: way too ambitious. 

Pat


> 
> Best,
> Richard
> 

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Received on Thursday, 13 September 2012 04:10:12 GMT

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