- Place and Time: M 6:00-9:00 PM, Bolton 213
- Instructor: Robin Smith (rasmith@tamu.edu)
- Office thereof: Bolton 314
- Telephone thereat: 845-5696

The subject of this course is the metatheory of propositional and predicate logic. This will include definitions of formal languages for these systems, their proof theory, model theory, and demonstrations of their soundness and completeness. As a necessary background for this, we will begin with an overview of the basic elements of set theory, including functions and relations, and a discussion of methods of mathematical proof.

- José L. Zalabardo,
*Introduction to the Theory of Logic*. Westview Press, 1999. ISBN 0-8133-6602-X

- Homework assignments (8): 20%
- Mid-term exam (take-home): 40%
- Final exam (take-home): 40%

In addition, we will work through a number of proofs in class. Understanding the nature of proofs in logical theory is a fundamental aspect of this course, and students will occasionally be asked to make presentations of proofs of theorems in class (with advance warning).

Page numbers refer to Zalabardo. Although I will try to stay reasonably close to this schedule, the pace may need to be adjusted depending on how the class goes.

- Aug. 29:
- (Introductory remarks, Basic set theory (1.1-1.3, pp. 1-8)

- Sept. 5:
- Mathematical proof; Relations and functions (1.4-1.7, pp. 8-32)

- Sept. 12:
- Functions (1.7), numbers (1.8).

**DO THESE EXERCISES: 1.15, 1.17, 1.24, 1.25, 1.26, 1.31, 1.32, 1.34**. Here are some Sample Answers - Language
*PL*: syntax (Ch. 2 sect. 1-2, pp. 36-49)

- Functions (1.7), numbers (1.8).
- Sept. 19:
- Syntactic metatheorems (Ch. 2 sect. 2-3)
- Semantics of
*PL*(Ch. 2 sect. 4, pp. 49-55)

- Sept. 26:
- Unique readability (2.5, pp. 55-60)
- Recursive Definitions, Expressive Completeness (Ch. 2 sect. 6-7, pp. 60-68)
**MID-TERM EXAM DISTRIBUTED**

- Oct. 3:
- Expressively complete languages (2.8, pp. 69-75)
- First-Order Logic (FOL): Syntax (3.1-3.2, pp. 76-90)
- MID-TERM EXAM DUE

- Oct. 10:
- FOL: Syntax (3.1-3.2, pp. 76-90)
- FOL: Semantics (3.3-3.4, pp. 90-101)
- Here are some Sample Answers for Exercises 3.19, 3.23, 3.27

- Oct. 17:
- FOL: Logical Consequence (3.5, pp. 102-108)
- FOL: Models (3.6, pp. 109-116)

- Oct. 24:
- FOL: Deductions--Basic and Connective Rules (4.1-4.2, pp. 117-122)
- FOL: Deductions--Propositional deduction (4.3, pp. 122-126)

- Oct. 31:
- FOL: Deductions--Substitution (4.4, pp. 126-132)
- FOL: Deduction--Quantifiers (4.5, pp. 132-134

- Nov. 7:
- FOL: Deducibility (4.6-4.7, pp. 134-140)
- FOL: Soundness (5.1, pp. 149-158)
- Here are some Sample Deductions (proofs of sequents) for the exercises in Exercise 3.22

- Nov. 14:
- FOL: Completeness (5.2, pp. 158-162)
- FOL: Completeness (5.2, pp. 158-162), one more time

- Nov. 21:
- FOL: Well-Rounded Sets (5.3, pp. 158-162)
- FOL: Negation Completeness (5.6, pp. 174-178)

- Nov. 28:
- FOL: Compactness (5.9, pp. 187-188)
- FINAL EXAM DISTRIBUTED

- Dec. 5:
- Monday: (This day is actually "redefined" as a Friday; hence, there is no class).
- Friday: FINAL EXAM DUE

Effective September 1, 2004, Texas A&M University has an Honor Code that defines campus policy on academic integrity and academic misconduct. The Aggie Honor System is charged with the enforcement of this Code. Students should be aware that the Aggie Honor System has the power to impose punishments for academic misconduct. For information on the Aggie Honor System, see http://www.tamu.edu/aggiehonor; information of particular concern to students, including definitions of types of academic misconduct, may be found at http://www.tamu.edu/aggiehonor/studentresources.php.

It will be my policy in this course to include the following statement on all examinations and request students to sign it:

"On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work." ________________________________ Signature of student

The Americans with Disabilities Act (ADA) is a federal antidiscrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact the Department of Student Life, Services for Students with Disabilities in Room 118 of Cain Hall, on the Internet at http://studentlife.tamu.edu/ssd/, or by telephone at 979-845-1637.