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Re: [ontolog-forum] Probabilistic Ontologies

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 17 Jun 2007 07:44:42 -0400
Message-id: <46751EAA.4030304@xxxxxxxxxxx>
Kathy,    (01)

What I was asking is how a language such as IKL, which is a
superset of FOL that also supports metalevel statements, could
be used to represent the kinds of operations required for
probability models.    (02)

> What you describe is far too simplistic.  It's nearly impossible
> to create a probability model that way that's not either utterly
> simplistic or inconsistent.    (03)

I used a very simple example, but the IKL mechanisms can be used
to support metalevel statements about propositions, the structural
components of propositions, their relationships to numerical
values, and the operations on those values.    (04)

> Over the past several decades, statisticians and computer
> scientists have learned a great deal about how to represent
> probabilistic knowledge.    (05)

I'm sure they have, but the IKL mechanisms can support those
representations.  Anything that can be defined in PR-OWL or
BayesOWL can be defined in IKL plus much, much more.  Numerical
functions of any kind can be defined in the Horn-clause subset
of IKL, which is a very efficient superset of OWL.    (06)

> Sophisticated probability can be thought of as having two parts:
> the structural and the numerical.  The structural part represents:
>  (1) a set of random variables (uncertain features or relationships);
>  (2) the possible values each random variable can take on); and
>  (3) conditional dependency relationships.    (07)

That could be represented in IKL.    (08)

> For example, suppose we are trying to identify aircraft using radar
> reports.  Consider two entities, a flying object and a sensor.  We
> have two random variables: ObjectType and SensorReport.  The possible
> values of each of these are {FighterAircraft, OtherAircraft, Bird}.
> The probability distribution for SensorReport depends on ObjectType.    (09)

Could you give a specific example of the representations that are
currently used (preferably in the usual math notation, not in OWL).    (010)

John    (011)

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