Math 470 - Mathematical Logic

Credits: 3

Course Description: Syntax and semantics of propositional and first-order predicate logic. Axiomatic theories and completeness. Brief discussion of incompleteness results.

Pre-Requisites: MATH 360 or MATH/CS 320L, or equivalent.

Current Textbook: Logic for Mathematics and Computer Science, by Stanley N. Burris, published by Prentice Hall, 1998. ISBN: 0-13-285974-2. Check with your instructor to make sure this is the textbook used for your section.

Mathematical background; history and role of logic. Propositions and truth tables. [1.1 - 1.2, 2.1 - 2.2]

Equivalence of propositional formulas. Replacement and substitution [2.3 - 2.6]

Validity and satisfiability of propositional formulas. Compactness [2.7 - 2.8]

Propositional proof systems [2.9]

Resolution. [2.10]

Equational Logic [3.1 - 3.3]

Predicate Logic [4.1, 4.2]

1st order logic - syntax and semantics [5.1 - 5.6]

Validity and satisfiability of 1st order formulas [5.7 - 5.11]

Proof systems for 1st order logic [6.1 - 6.3]

Consistency and Completeness [6.4 - 6.9]

Compactness and its consequences [6.10, 5.14]