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CSCI 8980: Computation and Deduction, Fall 2004
Online discussion using HyperNews
New Information:
- I have posted comments on the grading of homework 3 to the
homeworks page.
- Class presentations start on November 30. Information about these
is posted here.
Table of Contents
Contact Information
- Lecture Times and Place: TTh 12:45 - 2:00 p.m., Akerman Hall, Room 317.
- Instructor: Gopalan Nadathur
(gopalan@cs.umn.edu), EE/CSci 6-215, 612-626-1354.
Office Hours: TTh 2:30 - 3:30 p.m.
The main requirement will be mathematical maturity at the level
expected of a graduate student or a motivated undergraduate. In
particular, our discussions will require a facility with aspects of
discrete structures and formal arguments especially ones based on
induction. An interest in symbolic issues is also essential if the
course is to provide a fulfilling experience. No specific knowledge of
logic will be assumed. We will develop such knowledge as we go along.
Course Texts and References
There is no official textbook for this course. Some part of the
discussion will be based on research papers that will be distributed
during the term. The lectures on basic material draw on a number of
sources some of which are listed below:
- Melvin Fitting, First-Order Logic and Automated Theorem Proving,
Springer-Verlag. The book is available from Amazon. It will also be on
reserve at the Walter Library.
- J. Roger Hindley and J.P. Seldin. Introduction to
Combinators and Lambda Calculus, Cambridge University Press,
1990. Will be on reserve at the Math Library.
- J.-Y.
Girard, Y. Lafont and P. Taylor, Proofs and Types, Cambridge
University Press. The book is out of print but the authors have
made it available through the web as you can see.
There is another book by Jean Gallier that is available over the web
and that you might find interesting; it covers some of the ground we
will go over in this course but perhaps a little differently. The site
for this book and related papers is http://www.cis.upenn.edu/~jean/gbooks/logic.html.
There is a possibility that I will also make available my class notes
as the term progresses. This depends on how quickly I can typeset
them and how happy I feel about distributing them after I do this.
Course Description and Objectives
This course concerns computational aspects of logic. There are four
categories of topics that will interest us:
- The organization of reasoning processes. Here we will look at the
structure of reasoning systems such as natural deduction and sequent
calculi.
- The foundations of mechanized reasoning. Here we will look at
fundamental results such as Herbrand's Theorem and the Cut Elimination
Theorem that are the tools for showing the adequacy of our reasoning
systems. We will also study unification and possible organization of
proof procedures based on these results.
- Lambda calculi and their correspondence to proofs. Here we will
study lambda calculi as logical systems. Proofs that are the outcome
of deductions also correspond in interesting ways to lambda terms that
embody programs. We will understand this relationship between
computation and deduction.
- Computation through deduction. Some programming frameworks such
as logic programming use proof search directly as a vehicle for
computing. We will understand the essential ingredients of this idea
that may be referred to as "computation through proof search."
At the end of the course, we hope to have an appreciation for the
richness of logic on the one hand and for the several different ways
in which computational aspects interact with the notion of deduction
on the other.
This course will be divided between a standard lecture component and a
seminar part. Complementing the lectures, there will be homework
problems. The seminar part will require each of you to pick a topic
to study, to read a few research publications and then write a term
paper that you present in class. I will suggest some topics as the
term progresses, but you are also free to make your own
suggestions. The requirements for the topic are that it be related
broadly to kinds of views of deduction that we want to study in the
course and that it involves some new work (such as reading papers that
you don't already know the contents of) on your part. One specific
possibility that I should mention is that of writing a program that
realizes a proof procedure for some interesting logic or that realizes
relatively sophisticated operations on proofs or formulas. I
personally find this kind of thing quite exciting at least because I
really have to understand things to get the program right. Talk to me
if you would like to do something like this---I can give you ideas of
things to do.
The grade for the course will be determined by the assignments (25%),
the term paper (40%), the class presentation (25%) and class
participation (10%). The last component includes presence in class and
your role in discussions that take place, perhaps through HyperNews.
The term paper and presentation are obviously an important part of the
required work. Criteria that will be considered in evaluating them is
the comprehensiveness of the study, the coherence of the writeup and
the presentation and, most important, the special insights that
you offer into what you have read or worked on. It is impossible to do
a good job on these if you do not start early and work steadily. For
this reason, I would like you to adhere to the following timetable:
- Talk to the instructor about a possible topic before the end of
September.
- Select a topic and a couple of papers to read by Oct 19. Submit a
one page writeup by this date with this information.
- Be ready for a presentation by November 16. This presentation
should be of one class period in duration. Prepare the presentation
well since a quarter of the total points is allocated to this.
- Turn the term paper in by December 14. Again, take the task of
writing this report seriously since it carries 40% of the grade.
You should try to keep the size of the term paper within 20 pages.
Collaboration and Academic Honesty
Discussions related to the homework assignments and other parts of this
course are strongly encouraged. The HyperNews forums have in fact been
set up to facilitate this. However, any work that you turn in for
grade must be entirely your own. This means that you have to
exercise caution in determining what you can discuss. For instance, it
is okay to discuss homework problems so long as this is to understand
what is asked, but the discussion must stop before it gets to
considering answers. Similarly, when writing your term paper, you have
be very clear about what you have obtained from other sources:
generally, your perspectives and ideas that are valuable and that will
be evaluated. Violation of these principles will constitute a breach
of the academic honesty guidelines for this course. On the positive
side, you learn best when you think about and do things on your own
and this is what I would the emphasis to be on.
Last modified: November 30, 2004 by gopalan@cs.umn.edu