Re: [ontolog-forum] Probabilistic Ontologies

[Kathryn Blackmond Laskey <klaskey@xxxxxxx>]

At 9:45 AM -0400 6/16/07, John F. Sowa wrote:

> Kathy,
>
> In one sense, any ontology can be used with probabilities
> at the metalevel.  In IKL, for example, one could write:
>
>     (Prob (that (blue x)) 0.7)
>
> to say that the probability that x is blue is 0.7.

Of course!  But see below.

> This
> method keeps the ontology and the probabilities completely
> separated:  Nothing inside the proposition marked by
> "that"
> mentions any probabilities, and the probability expressions
> outside the proposition do not use the types and
> relations
> of the ontology.

Lots of people have tried to develop formalisms that combine probability and logic.  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.

Over the past several decades, statisticians and computer scientists have learned a great deal about how to represent probabilistic knowledge.  There are some extremely sophisticated applications that can do very interesting things.  Companies such as Google, Microsoft, and Intel are investing heavily in Bayesian technology, and have vibrant Bayesian reasoning groups.  They make those investments because the technology works.  I have heard many impressive "in the hallways" anecdotes, most of which I'm not at liberty to repeat because of proprietary or security concerns.  Suffice it to say that well-engineered Bayesian models have been found to be able to do things people thought you couldn't do with computers, and in some cases these models have out-performed the human analysts on whose knowledge they were based.

These success stories could not have been achieved with systems that simply allowed you to annotate logical statements with probabilities.  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.

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.  It may also depend, for example, on the cloud cover and whether the opposing military force is jamming your sensors.  This would require a model with random variables CloudCover with possible values {None, Light, Heavy}, and Jamming with possible values {Yes, No}.  Then we would need a probability distribution for SensorReport that would depend on CloudCover, Jamming, and ObjectType.

Bayesian networks represent a set of random variables, their possible values, the dependence relationships, and the probability distribution of each random variable given the random variables it depends on.  A Bayesian network represents a consistent joint probability distribution on all these random variables.  If I learn something about one of them, Bayes Rule gives me an updated distribution on all the others.

BayesOWL, developed at University of Maryland, lets you represent a Bayesian network as an OWL ontology.  It does more than just attaching a probability to a logical statement.  It represents all the information I described above -- the random variables and possible values, the dependency structure, and the conditional distributions for the random variables as a function of the values of their parents.

But Bayesian networks aren't expressive enough for interesting problems.  For example, consider a scenario in which there are three fighter aircraft, two other aircraft, seven birds, and four sensors.  Each of the flying objects is in range of some of the sensors but not others.  We don't know which object a given sensor is looking at. The objects are moving in and out of range of the sensors.

Now consider a problem in which there are n fighter aircraft, m other aircraft, k birds, and r sensors, where n, m, k and r are unknown.

It can get a lot more complicated than that!!!  For example, the error probability of the sensor might depend on the distance of the object from the sensor, or the angle from which the object is being viewed.

To reason about these kinds of problems, you need a much tighter integration with the ontology than just attaching probabilities to logical statements.

> KBL> My colleagues, students and I have built several toy
>  > probabilistic  ontologies.  I've worked with
> colleagues
>  > to build artifacts that were called "probability
> models"
>  > but had features that one associates with ontologies,
> i.e,
>  > were built in expressive probabilistic languages with
> have
>  > types and individuals, subtypes and inheritance,
> attributes
>  > and relations.
>
> Do you and your colleagues integrate the probabilities with
> the ontology more directly?

Yes.  There are now many highly expressive probabilistic languages.  Probabilistic relational models, object-oriented Bayesian networks, Bayesian logic programs, plates, and lots more.  People have been working intensively on integrating probability and logic over the past couple of decades.  Much progress has been made.

That's what PR-OWL is about.

> If so, could you give some
> examples to show how they interact more
> closely than the
> IKL example above.

I hope the example above helps.  See some of our papers on PR-OWL for more on this.  Paulo Costa and I are working on some expository examples, which will be posted on the PR-OWL web site.  But there are only so many hours in the day...

Kathy

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