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Monotonicity of semantic extensions (was: Re: Test cases and examples for dataset entailment)

From: Richard Cyganiak <richard@cyganiak.de>
Date: Wed, 12 Sep 2012 16:19:39 +0100
Cc: public-rdf-wg@w3.org
Message-Id: <E6E32E4C-19DC-4148-B80C-D86980DC73CC@cyganiak.de>
To: Antoine Zimmermann <antoine.zimmermann@emse.fr>
Hi Antoine,

This is no longer about the minimal dataset semantics, but it's a topic that I'm interested in, so let's go on if you don't mind.

As usually, I'm learning this stuff as I'm going along, and I'm probably just clueless about what it means for Y to be a proper semantic extension of X.

On 11 Sep 2012, at 22:11, Antoine Zimmermann wrote:
> I realise that we, and others, may not have the same idea of what a proper semantic restriction is. For me, a semantic restriction is, for instance, what RDFS is to RDF, what D-entailment is to RDFS and what OWL Full is to D-entailment.

For me too.

> With the direct graph semantics you propose, it is a non-monotonic extension because when you switch this semantics on, the entailments you could do with the "minimal" semantics are not valid anymore.
> I don't think that's how people think of an extension. They probably do not expect that extensions make you lose what you had before.

Well, yes, there are cases where the minimal semantics says that A entails B, and the “direct graph” semantics says that A contradicts B.

> It also means that people who do not use the extension get conclusions contradicting those who use the extension. This is not the case with RDFS, OWL, etc. If you do not use D-entailment, you are not going to get any conclusions that contradicts those who use it. And those who switch the D-entailment semantics on do not lose anything they could conclude without it.

Is this so? It seem to be not quite true. Example:

    :p rdfs:range xsd:integer.
    :s :p "aaa"^^xsd:integer.

Under RDFS-entailment, I can conclude from that graph:

    "aaa"^^:xsd:integer a xsd:integer.

But when we switch on D-entailment, that triple is now a contradiction, I believe. So what used to be an entailment is now a contradiction.

Contrast that with my direct graph example:

    { :g1 a rdf:Graph }
    :g1 { :s :p :o }

Under simple-dataset-entailment, this entails

    :g1 { :p :p [] }

Under simple-dataset-plus-direct-graph-entailment, that becomes a contradiction. So it seems equivalent to the situation above?

There's obviously some subtle distinction here that I'm missing. Can you formally state the conditions that a semantic extension of E-dataset-entailment has to meet in order to be considered a proper semantic extension?

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. It also seems to fold various separate issues into one lemma, making it hard to understand. There's also [3] but I don't know how that translates to the case of E-dataset-entailment.

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.

Best,
Richard


[2] http://www.w3.org/TR/rdf-mt/#MonSemExt
[3] http://www.w3.org/TR/rdf-mt/#glossMonotonic

> 
> I understand that you wrote this merely as an example, and it indeed proves that such semantics can be defined as a semantic extension of our "minimal" proposal. I provided similar things myself already [1]. But even when I was writing this, I was not convinced by the utility. I only used it as a proof that it can be done, formally.
> 
> 
> [1] http://www.w3.org/2011/rdf-wg/wiki/TF-Graphs/Dataset-semantics
> 
> --AZ
> 
>> 
>>> If I had to directly talk about a graph in a named graph, I would
>>> do it like this:
>>> 
>>> :g  a  sd:Graph; :validityTime  "1998-09-11"^^xsd:date; ... :g  {
>>> :bob  :employedBy  :ibm }
>>> 
>>> It works, as long as I am using an agreed upon, explicit
>>> specification of a shared conceptualisation, a.k.a. an ontology.
>> 
>> Yeah, and that's exactly the example I gave, except I called it
>> rdf:Graph instead of sd:Graph, and formalized the implicit assumption
>> that :g actually denotes { :bob :employedBy :ibm } as opposed to some
>> other graph. You can't do that just by defining an ontology.
>> 
>> The benefit of formalizing this is that, for example, if I define a
>> Turtle datatype then it will just work, and I can infer
>> 
>> { :g owl:sameAs ":bob :employedBy :ibm"^^xxx:Turtle }
>> 
>> from the dataset above, modulo namespace declaration.
>> 
>> Best, Richard
>> 
>> 
>> 
>> 
>>> 
>>> 
>>> AZ.
>>> 
>>> 
>>> 
>>> 
>>> Le 11/09/2012 11:46, Richard Cyganiak a écrit :
>>>> On 10 Sep 2012, at 17:30, Richard Cyganiak wrote:
>>>>> Two other things that I'd quite like to see before we can call
>>>>> the proposal complete:
>>>>> 
>>>>> 1. Some thinking on how it addresses our graph use cases. (Do
>>>>> we have an “official” list of those? I've lost track with all
>>>>> the various documents.)
>>>>> 
>>>>> 2. Some examples for semantic extensions, in order to show that
>>>>> various other proposed semantics can actually be done as proper
>>>>> semantic extensions of this minimal dataset semantics.
>>>> 
>>>> I've worked a bit on this item and made attempts to formalize
>>>> three semantic extensions:
>>>> 
>>>> * owl:imports (formally explains how owl:imports works in RDF
>>>> datasets) * web datasets (formally defines that stuff published
>>>> on the web is asserted) * direct graph semantics (permits
>>>> "literal" immutable graphs)
>>>> 
>>>> http://www.w3.org/2011/rdf-wg/wiki/TF-Graphs/Minimal-dataset-semantics#Possible_Semantic_Extensions
>>>> 
>>>> 
>>>> 
> I'm not proposing that we should standardize any of this; the intention is merely to explore how flexible/extensible the semantics proposed on that page is.
>>>> 
>>>> Again, I'm not really good at this formal semantics stuff, so
>>>> this might all be spectacularly wrong.
>>>> 
>>>> Best, Richard
>>>> 
>>> 
>>> -- Antoine Zimmermann ISCOD / LSTI - Institut Henri Fayol École
>>> Nationale Supérieure des Mines de Saint-Étienne 158 cours Fauriel
>>> 42023 Saint-Étienne Cedex 2 France Tél:+33(0)4 77 42 66 03
>>> Fax:+33(0)4 77 42 66 66 http://zimmer.aprilfoolsreview.com/
>>> 
>> 
>> 
> 
> 
> -- 
> Antoine Zimmermann
> ISCOD / LSTI - Institut Henri Fayol
> École Nationale Supérieure des Mines de Saint-Étienne
> 158 cours Fauriel
> 42023 Saint-Étienne Cedex 2
> France
> Tél:+33(0)4 77 42 83 36
> Fax:+33(0)4 77 42 66 66
> http://zimmer.aprilfoolsreview.com/
> 
Received on Wednesday, 12 September 2012 15:20:09 GMT

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