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Re: How many axioms?

From: Jeremy Carroll <jjc@hpl.hp.com>
Date: Mon, 23 Jan 2006 09:20:17 +0000
Message-ID: <43D49FD1.903@hpl.hp.com>
To: Gong Cheng <gcheng@seu.edu.cn>
CC: Semantic Web W3C <semantic-web@w3c.org>

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 Monday, 23 January 2006 09:22:30 UTC

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