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Computer Science 226	   Representation Theory        Winter 1974
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\J	This course is concerned with the problem of representing information
in the memory of a computer so that programs can use this information to
behave intelligently.  I have been pushing the importance of this problem
for fifteen years, but now there is general recognition that this is a key
problem for artificial intelligence.

	 The information to be represented is what a program can know
and must  know in order to solve some  class of problems of interest.
The meaning  of the  phrase \F1must  know\F0 is  evident, but  \F1can
know\F0  require  explanation.    First,   the  information  must  be
obtainable  by  observation, by  communication  or  by reasoning.
Second, the information  must be plausibly present.   Thus it is  not
plausible that most people  have specific information about how to go
from Fresno to Miami, but it is plausible that they have  information
about travel within the United States adequate to solve that problem.
Third,   the information must be present in  a form adequate to solve
the problems.

	The importance of representation problems stems from the fact
that inadequacy of the representations used is the main reason for the
limitations of present programs in artificial intelligence.

\F2Some illustrations of the above contention\F0

	While the importance of the representation problem now has wide
agreement among people working in AI, there is much confusion and little
agreement on what is the best approach towards solving it.  In particular,
there is the controversy over whether declarative representations,
procedural representations, "analogical representations" or still others
are best.  This course will take declarative representations as primary,
but other schools of thought will be represented by guest lecturers.
Within the declarative school, there is further controversy over whether
a system of mathematical logic is the right way to proceed or whether
something based on ordinary language  might work better.  This course
will mainly explore the possibilities of mathematical logic, but we
will hear from the others too.

	The formalisms of mathematical logic require practice for their
effective use and no-one has enough practice.  Even mathematical logicians
do very little of their work within the logical formalisms - most of it
is informal mathematics proving things \F1about\F0 the formal systems.
Because of this, the existing formalisms are not very convenient and
require improvement in various respects.  Which respects are not entirely
easy to determine without more practice in using them.  

	A good part of the work in the course will consist of expressing
facts involved in common sense problems and their solution in first
order logic with set theory and proving that a proposed solution to
the problem really is one.  For this purpose, we will use \F2FOL\F0, a proof
checker for an expanded first order logic written and being further
developed by Richard Weyhrauch of the Stanford Artificial Intelligence
Laboratory.  Computer and terminal time at the Lab will be made available
and there will be some terminals on campus.

	There will be no teaching assistant in the course, but my secretary,
Mrs. Kasee Menke will have available handouts and other material concerning
the course.

	Reading material includes the following:

	1. The \F2FOL\F0 manual which will be distributed.

	2. Three papers, \F1Programs with Common Sense, Situations, Actions
and Causal Laws,\F0 and \F1Some Philosophical Problems from the Standpoint
of Artificial Intelligence\F0 which give the basic approach to the representation
problem at five year intervals.
These will also be distributed.

	3. Papers by Erik Sandewall, Marvin Minsky, and others which will be
on reserve in the computer science library.

	4. On mathematical logic, the following books are recommended:
\F1Mathematical logic and formalized theories:  A Survey of Basic Concepts and 
Results\F0 by Robert Rogers.  This covers the main topics on a rather
informal level since it is written for philosophers.  \F1Set Theory
and the Continuum Hypothesis\F0 chapters 1 and 2 by Paul Cohen.  This contains
one of the most usable approaches to the axiomatization of set theory.  Of
course, this course is not concerned with the continuum hypothesis itself
which is Cohen's main objective in the book.  Because the main emphasis
of the course is in expressing facts about other matters within logic,
no mathematical book has the right emphasis for our present purposes.
We need a new Sylvanus Thompson to write \F1Mathematical Logic for the
Practical Man\F0.  The electrical engineers are no help here, because their
interest in logic concerns only propositional logic whereas our main interest
will be in predicate calculus.

	5. Philosophers have treated some of the questions we are interested
in here.  Their point of view may be typified by the question "What is knowledge"
whereas we shall be interested in "How can we formalize enough about knowledge
so that we can express facts about reservation clerks knowing airline schedules
and telephone numbers being "in" the telephone book.  Nevertheless, despite
the difference in point of view, there is a vast philosophical literature which
is described in the last section of \F1Some Philosophical Problems from the standpoint
of Artificial Intelligence.\F0\.