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RE: Question about problems with top/bottom property

From: Michael Schneider <schneid@fzi.de>
Date: Mon, 2 Jun 2008 16:02:24 +0200
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A096B090@judith.fzi.de>
To: "Rinke Hoekstra" <hoekstra@uva.nl>
Cc: <public-owl-wg@w3.org>
Rinke Hoekstra wrote:

>Do we already have some idea of the consequences of adding the bottom
>property, computationally speaking?
>
>As I understand, we can already simulate topprop using existing
>constructs, can we do the same for botprop?

Hm, from my layman's perspective, BOTTOM looks pretty innocent to me. 

It's easy to define within OWL:

    PropertyDomain( BOTTOM owl:Nothing )
    PropertyRange( BOTTOM owl:Nothing )

And we don't even need owl:Nothing, since we can define our own 
EMPTY class just based on class inclusion, intersection and complement:

    SubPropertyOf( EMPTY IntersectionOf( X ComplementOf(X) ))

for some arbitrary class X.

Also, the semantic properties of BOTTOM look pretty simple.
For example:

  * Using it in property assertions will always lead to unsatisfiability.

  * Each "Some BOTTOM . C" restriction equals the empty class. 

  * Each "All BOTTOM . C" restriction equals the universe.

  * Using it as the LHS of a role inclusion axiom is redundant.

  * Using it as the RHS of a role inclusion axiom makes the
    LHS property equivalent to BOTTOM.

But, of course, I only look at the surface here. Maybe there
are deeper problems lurking around? Boris?

>-Rinke

Cheers,
Michael

>Tracker: this is related to ISSUE-112



Received on Monday, 2 June 2008 14:03:10 GMT

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