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Universal Quantification - common misconception

From: Niall Murphy <nimurphy@gmail.com>
Date: Tue, 22 Mar 2011 11:18:23 +0000
Message-ID: <AANLkTim4XdrjkbP_91w=CcMfUNTbZmv-6rACqhhgwhaY@mail.gmail.com>
To: public-owl-dev@w3.org

I am confused by the statement in the OWL 2 Primer that "any individual that
is not a “starting point” of the property hasChild is class member of any
class defined by universal quantification over hasChild.", referring to this

    ObjectAllValuesFrom( :hasChild :HappyPerson )

My understanding (or attempt thereof) is that the any individual that is not
not a "starting point" of the property hasChild can be expressed as follows:

        :ObjectSomeValuesFrom(:hasChild :Person)

And the class of individuals defined by universal quantification over
hasChild as follows:

    ObjectAllValuesFrom(:hasChild QualoverHasChild)

So because NotStartingPointOfHasChild has no individuals who are members of
:UniversalQualificationOverHasChild, or to put it another way, all none of
them are related to UniversalQualificationOverHasChild by hasChild, they all
meet the restriction and are therefore members.

If the above is true, does the solution of including an
ObjectSomeValuesFrom(:hasChild :HappyPerson) restriction in the example
class expression prevent entailment of a paradox, or have I just been
spending too long looking at OWL semantics?

Received on Wednesday, 23 March 2011 08:07:27 UTC

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