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"[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx> |
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From: |
Kathryn Blackmond Laskey <klaskey@xxxxxxx> |

Date: |
Sat, 16 Jun 2007 14:00:45 -0400 |

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<p06110405c299ce41c458@[192.168.0.103]> |

At 9:45 AM -0400 6/16/07, John F. Sowa wrote:
Kathy, Of course! But see below. This 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.
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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