Computation and Deduction

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.

- Contact Information
- Prerequisites
- Texts and Reference Books
- Course Description
- Required Work and Grading
- Homeworks for Fall 2004
- Academic Honesty

- 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.

- 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 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.

- 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."

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.

Last modified: November 30, 2004 by gopalan@cs.umn.edu