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Re: How many axioms?

From: Gong Cheng <gcheng@seu.edu.cn>
Date: Wed, 25 Jan 2006 18:27:50 +0800
Message-ID: <008301c6219a$00e25170$6a0977ca@petercheng>
To: "Jeremy Carroll" <jjc@hpl.hp.com>
Cc: "Semantic Web W3C" <semantic-web@w3c.org>
Thanks Jeremy and all. I have found those misconceptions!

Gong

> 
> Noting that this has not had any replies on the list...
> 
> In the OWL abstract syntax, there are many equivalent ways of saying the
> same thing. (This is not unusual, but fairly inevitable).
> 
> In the RDF triple syntax for OWL there are many equivalent ways of
> saying the same thing.
> 
> The mapping rules from section 4 of the OWL Semantics and Abstract
> Syntax define a many-to-many relationship between these two syntaxes for
> OWL.
> 
> Thus there are many cases where we have two equivalent abstract syntax
> forms for an ontology A1 and A2 with different number of axioms, which
> both are related by the mapping rules to the same set of triples T1.
> (There may also be T2, T3, ..., which are also equivalent sets of triples).
> 
> So your question is based on a misconception that it is possible to ask
> how many axioms in the abstract syntax form of a set of triples.
> There is not a single abstract syntax form, there are many.
> The different abstract syntax forms can have different number of axioms.
> 
> Jeremy
> 
> Gong Cheng wrote:
>> Hi all,
>> 
>> I was confused about the axioms in OWL.
>> 
>> For example,
>> supposing exp:foo, exp:bar1 and exp:bar2 were three OWL class names, and there were three triples:
>> 
>> exp:foo rdf:type owl:Class
>> exp:foo rdfs:subClassOf exp:bar1
>> exp:foo rdfs:subClassOf exp:bar2
>> 
>> so how many OWL axioms are there in these two triples (i.e., how many OWL axioms can be transformed to these triples)?
>> 
>> And my opinion:
>> Answer 1: two axioms.
>> The first two triples indicates:
>> axiom ::= 'Class(' classID  ['Deprecated'] modality { annotation } { description } ')'
>> and the last triple indicates:
>> axiom ::= 'SubClassOf(' description description ')'
>> (The last two triples can exchange)
>> 
>> Answer 2: only one axiom, i.e.,
>> axiom ::= 'Class(' classID  ['Deprecated'] modality { annotation } { description } ')'
>> 
>> Actually, the triple involving rdfs:subClassOf seems can be transformed to part of either axiom. And if Answer 2 was right, why we still need axiom ::= 'SubClassOf(' description description ')'?
>> 
>> Thanks in advance!
>> 
>> Regards,
>> 
>> Gong Cheng
>> 
>> -------------------------------------------------------------
>> Gong Cheng
>> Department of Computer Science and Engineering
>> Southeast University, Nanjing, P.R.China
>> Phone:        +86-(0)25-83793235
>> Fax:          +86-(0)25-83794838
>> E-mail:       gcheng@seu.edu.cn
>> Address:      Department of Computer Science and Engineering
>>               Southeast University
>>               Nanjing 210096, P.R.China
>> -------------------------------------------------------------
>> 
>> 
> 
> 
> 
>
Received on Wednesday, 25 January 2006 10:34:47 UTC

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