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

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”.

<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.

> 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. 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?

> 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.)

>> 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). 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, 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.

Best,
Richard

Received on Wednesday, 12 September 2012 20:04:58 UTC