# RE: About RDFS axiomatic triples

From: Michael Schneider <schneid@fzi.de>
Date: Mon, 14 Jul 2008 11:24:28 +0200
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A0A26646@judith.fzi.de>
To: "Wei Tai" <taiw@cs.tcd.ie>
Cc: <semantic-web@w3.org>, "Li Ding" <dingl@cs.rpi.edu>
```Hi, Wei,

Li Ding answered to Wei Tai:

>2. you can surely infer that according to RDF semantics specification
>section 4.1, http://www.w3.org/TR/rdf-mt/#rdfs_interp
>
>since the following triple must be true in all rdfs-interpretations
>    rdf:List rdf:type rdfs:Class .

This triple (which is not an axiomatic triple) can be inferred, for example,
the following way:

Start from the RDF axiomatic triple

(1) rdf:nil rdf:type rdf:List
(1') <I(rdf:nil), I(rdf:List)> is in IEXT(I(rdf:type))

(both given forms have the same meaning), and the RDFS axiomatic triple

(2) rdf:type rdfs:range rdfs:Class
(2') <I(rdf:type), I(rdfs:Class)> is in IEXT(I(rdfs:range))

Apply to (1') and (2') the RDFS semantic condition for rdfs:range :

(3) IF <x,y> is in IEXT(I(rdfs:range)) AND <u,v> is in IEXT(x)
THEN v is in ICEXT(y)

Which provides you:

(4) I(rdf:List) is in ICEXT(I(rdfs:Class))

Now apply to (4) the RDFS semantic condition for rdf:type :

(5) x is in ICEXT(y) IF-AND-ONLY-IF <x,y> is in IEXT(I(rdf:type))

which results in

(6) <I(rdf:List), I(rdfs:Class)> is in IEXT(I(rdf:type))

And that's equivalent to stating:

(6') rdf:List rdf:type rdfs:Class

Cheers,
Michael

>you can infer your triple using the following RDFS semantic condition
>
>IC = ICEXT(I(rdfs:Class))
>
>If x is in IC then <x, I(rdfs:Resource)> is in IEXT(I(rdfs:subClassOf))
>
>best,
>Li
>
>
>On Sun, Jul 13, 2008 at 5:59 PM, Wei Tai <taiw@cs.tcd.ie> wrote:
>>
>> Hi All,
>>
>> I notice that the RDFS axiomatic triple set provided by the document
>"RDF
>> semantics" do not contain the triple
>>   rdf:List rdfs:subClassOf rdfs:Resource
>> , but I can not infer this triple out from other existing triples in
>that
>> set. Do I miss something or we should add this triple into that
>axiomatic
>> triple set?
>>
>> Thank and Best Regards
>> Wei
>>
>> --
>> Wei Tai
>>
>>
>>
>>
>>
>
>
>
>--
>Li Ding
>http://www.cs.rpi.edu/~dingl/

```
Received on Monday, 14 July 2008 09:25:09 UTC

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