Georgia Institute of Technology

School of Public Policy

Program in Philosophy, Science, & Technology

Fall 2000

PST 4903 SPECIAL PROBLEMS: MATHEMATICAL LOGIC

FALL SEMESTER, 2002

D.M. SMITH TH 11.00-13:30am ROOM 217

*Professor Lorenzo Magnani*

*Office: 217 DM Smith*

*Phone: 404-894-9050 (Office) *

*E-mail: *__lorenzo.magnani@cc.gatech.edu__

Office hours: T 12:00-3:00pm and by appointment

**DESCRIPTION**

Propositional logic. First order logic. Gödel theorem. Resolution calculus. Nonmonotonic logic. Elementary modal logic. Introduction to logic programming.

REQUIREMENTS

Students will be required to make a presentation and to write three papers. Grades will be determined as follows:

Presentations and/or class participation: 40%

Papers: 60%

Due dates for assignments are firm deadlines.
They are announced well in advance, so please plan accordingly. There is
no room in the schedule to fall behind in either reading or writing assignments.
Institute regulations do not allow the grade of incomplete to be given except
in cases of extreme emergency. Students are expected to adhere to the Student
Honor Code. __Your signature (which should be on all written work) is understood
to be your affirmation that the work is yours. Please indicate your SSN
number in capital.__

**Essays**: The text of the papers should
be between 1500 and 2000 words in length, typed, double-spaced, 12 point
font, page numbers, stapled, and word count included with your name. Do not
exceed the word limit by more than 100 words. Provide citations for all quotations
and sources used (not included in word count). Do not use extensive quotations.

**Presentations**: These will be made
in groups of 3-5 students weekly. Please do not simply summarize the readings.
Presentations should have two parts: 1. address what you take to be the main
problems of the author(s) and their proposed solutions (taking not more
than ½ hour) and 2. provide a set of problems formulated by your group for
discussion. You should provide a short handout (with your names written on
it) to me and the class with a list of the problems for discussion.

**August 20 and 22 **: *Set theory
and propositional calculus .*

**August 27** **and 29**:* Propositional
culculus..*

**September 3** **and 5**: *First
order logic. Intutive introduction.*

**September 10** **and 12**: *First order logic. Language.**.*

**September 17 and 19**:** ***First order logic. Semantics**.*

Paper 1 due by noon Tuesday September 24 (my mailbox, Smith Building).

**September 24 and 26:** *First order logic. Axiomatic Systems**.*

**October 1 and 3**: *Gödel theorem.*

**October 8 and 9**: *Gödel theorem.*

**October 15 (MID-TERM, no classes)
and 17**:

**October 22 and 25: *** Resolution
calculus.*

**October 29 and 31: *** Resolution calculus.*

**Paper 2 due by noon Thursday November
5 (my mailbox, Smith Building).**

**November 5 and 7: ***Nonmonotonic
logic.*

**November 12** **and 15**: ** ***Nonmonotonic logic.*

**November 19 and 21**:* Elementary
modal logic.*

**November 26 and 23: ***Introduction
to logic programming.*

**December 3** **and 5**: ** ***Introduction to logic programming.*

(Final) paper 3 due by noon Friday December 5 (my mailbox, Smith Building).

REQUIRED TEXTS

M.L. SCHAGRIN, W.J. RAPAPORT and R.R. DIPERT, *Logic:
A Computer Approach*, McGraw-Hill, New York, 1985.

E. MENDELSON, *Introduction to Mathematical Logic*,
D. Van Nostrand Company, Princeton, NJ, 1964.,

L. MAGNANI and R. GENNARI, *Manuale di logica.
Logica classica e del senso comune*, Guerini, Milan, 1997.

M.R. GENESERETH and N.J. NILSSON,* Logical Foundations
of Artificial Intelligence*, Morgan Kaufmann, Los Altos, CA, 1987.