ACTION-178: What is ISSUE-116 (Axiomatic Triples for OWL R) about?

[cc'ing Ivan Hermann as the raiser of ISSUE-116.]

Dear WG!

At F2F3, ACTION-178 was put on me to explain my understanding of

  ISSUE-116: "Should Axiomatic Triples be added to OWL-R Full?"

Here is my understanding, after a short explanation what axiomatic triples are.

(A) What are axiomatic triples?
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These are typical examples of axiomatic triples (taken from RDFS):

  (1) rdf:Property rdf:type rdfs:Class
  (2) rdf:type rdf:type rdf:Property

These axiomatic triples specify the part of the universe to which certain URIs of the "system vocabulary" belong: 'rdf:Property' denotes a class, while 'rdf:type' refers to a property. 

Note that in RDF, there is no real distinction between the vocabulary specifying the language (such as 'rdf:type'), and the custom vocabulary used within an ontology. Axiomatic triples interpret the system vocabulary, by telling what's true for them independently of the concrete ontology, in which they are used.

Axiomatic triples are defined in RDF and RDFS, and also in pD*. OWL 1 Full also contains lots of axiomatic triples for the OWL vocabulary, though they are written in a different notation there.

(B) Which axiomatic triples do typically exist?
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Aside of type information (as in the examples (1) and (2)), RDFS also specifies the domain and range for all properties in the RDFS vocabulary, e.g.:

  (3) rdf:type rdfs:domain rdfs:Resource
  (4) rdf:type rdfs:range rdfs:Class

(C) What is the scope of the issue?
-----------------------------------

The main question at F2F3 was whether this issue is also about *additional* genuine OWL R Full axiomatic triples, or just about RDFS axiomatic triples. From Ivan's mail it becomes pretty clear that this issue includes axiomatic triples, which go beyond RDFS (Ivan confirmed this to me in a private mail). One of his stated examples is:

  "owl:FunctionalProperty,rdfs:subClassOf,rdf:Property"

This assertion clearly does *not* exist in RDFS, since 'owl:FunctionalProperty' doesn't belong to the RDFS vocabulary. (Whether this example would be a useful axiomatic triple or not for OWL R Full is not a topic here.)

(D) What would be the additional axiomatic triples?
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Defining axiomatic triples is in most times a pretty straight forward task. For all OWL URIs in the OWL R vocabulary the type is stated (Resource, Class, Property), and for properties also the range and domain. All axiomatic triples which I have in mind would follow the examples (1) to (4) above.

For example, for 'owl:complementOf', I would propose the axiomatic triples:

    owl:complementOf
        rdf:type rdf:Property ;
        rdfs:domain rdfs:Class ;
        rdfs:range rdfs:Class .

Since OWL 2 Full will also have axiomatic triples (the old ones from OWL 1 Full, and new ones for the new vocabulary), OWL R Full can simply take what it needs from OWL 2 Full.
 
(E) Could additional axiomatic triples lead to problems?
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I suppose that if RDFS axiomatic triples do not already lead to problems, then additional axiomatic triples for the OWL R vocabulary will not lead to problems, either.

In general, I expect axiomatic triples, as long as they have the form given in (D), to be semantically harmless (well, mostly harmless :)).

>From a spec'ing effort perspective, adding them is an easy task (I am offering to do this, should the WG decide to add them).

Regards,
Michael

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
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Email: Michael.Schneider@fzi.de
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