Logic, Language, and Information

			Lawrence S. Moss


"The class introduces a wide variety of mathematical topics pertinent to
cognitive science, artificial intelligence, and related fields. Those
topics are primarily taken from probability and linear algebra, and
secondarily from logic, algorithms and complexity theory, and
optimization. The intended applications will be to models for uncertain
reasoning, such as Bayesian nets and other graphical models, hidden Markov
models, and some types of neural nets. In addition, the class will also
present the basics of logic, both in its classical form and some systems
for areas like default reasoning. It will also introduce concepts like
entropy and game-theoretic equilibrium. So the class will see many
application areas. But it will not be a class in using or even building
application tools. And although the applications include some of the main
tools in cognitive science and artificial intelligence, the overall point
is to introduce a large body of related mathematical ideas in a friendly
way, so that you will be stimulated to continue learning."

I am lecturing from slides that go on a web site, and you can have a look
at any time:

           http://math.indiana.edu/home/moss/Q520.htm

I do not want to propose a firm day-by-day outline for the one week
NASSLLI course yet.  However, here is a tentative schedule that is
plausible:

Day 1: Hopfield nets, review of probability, Bayesian nets (examples and
properties, but not the algorithm for inference). For probability, I could
follow John Goldsmith's notes on Probability for Linguists.

Day 2: More on probability, Markov chains, Hidden Markov models,
probabilistic regular languages and perhaps probabilistic cfg's.

Day 3: The basics of Information Theory, including the a discussion of
results like the Paris-Vencovska theorem connecting maximum entropy with
logic.  If possible, it would be nice to say something about the EM
algorithm on this day, following Detlef Prescher's ESSLLI course notes.

Day 4: The basics of Neural nets, with some applications, especially in
linguistics. Also, some systems of default reasoning and connections to
probability.  Indeed, default reasoning and reasoning about uncertainty
are some of the things people should take away from the course.

Day 5: The emergence of logic.  The goal is to present work by Gardenfors,
Blutner and others on the relation of connectionist models with logic.
(Alternatively, one could do connections of dynamic modal logic and
probability.)