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Re: 4.5 InverseOf: a test case for mapping between ontologies

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Thu, 6 Jun 2002 10:08:21 +0100
Message-ID: <15615.9861.514187.494394@merlin.oaklands.net>
To: Evan Wallace <ewallace@cme.nist.gov>
Cc: www-webont-wg@w3.org

On May 29, Evan Wallace writes:
> 
> 
> The issue states:
>   InverseOf is a highly used (some say misused) feature of DAML+OIL. The 
>   OWL-Full proposal left it out, because of some worries on the part of some 
>   participants that it caused some logical problems for users.  Other people 
>   argue it is an important expression in the mapping between ontologies.
> 
> Dan Connolly wrote:
> >So I propose to close this issue
> >http://www.w3.org/2001/sw/WebOnt/webont-issues.html#4.5-InverseOf
> >by approving this test case and the
> >existing specification of inverseOf:
> >
> >"if the pair (x,y) is an instance of P, than the pair (y,x) is an
> >instance of the named property."
> 
> I propose that we not close any issues without a full discussion
> of problems motivating their raising.  Since the "logical problems for 
> users" are not enumerated in the issue document, someone needs to 
> describe them for us so we can judge if Dan's uncompelling example 
> justifies ignoring them.  If no logical problems can be described
> or shown by example, then I propose that we close the issue on the 
> basis that there is no demonstrable problem with the language
> feature: inverseOf.

The main problem with inverse is that, in combination with
extensionally defined classes (oneOf), it increases the complexity of
providing reasoning support for the language. We know that the
combination of inverse and oneOf causes worst-case complexity for the
class consistency problem to jump from ExpTime to NExpTime. Moreover,
there is no known "practical" algorithm for this logic (i.e., one that
seems likely to lend itself to implementations with good typical case
performance), and no implemented systems.

Getting rid of either inverse or oneOf solves the theoretical problem:
there are no implemented systems for the language with oneOf and
without inverse, but a "practical" algorithm is known; there are
several implemented systems for the language with inverse and without
oneOf.

Regards, Ian

p.s. Details about algorithms and complexity can be found at:

http://www.cs.man.ac.uk/~horrocks/Publications/download/2001/ijcai01.pdf

> 
> Also, if the above quoted text is a specification, then what is P and 
> where is the the object property named.  Suggest that the final OWL
> specification should include a proper EBNF syntax specification.
> 
> >I think inverseOf is quite useful for mapping
> >between ontologies; here's
> >an example of how I understand it to work:
> >
> >premise:
> >
> > :joe my:hasBrother :bob.
> 
> A completely asymmetric property such as hasParent would make a better 
> example for inverseOf.
> 
> >
> > my:hasBrother ont:inverseOf your:isBrotherOf.
> >
> >conclusion:
> >
> >
> >  :bob your:isBrotherOf :joe.
> 
> 
> Evan K. Wallace
> Manufacturing Systems Integration Division
> ewallace@nist.gov
Received on Thursday, 6 June 2002 05:11:02 GMT

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