m!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> Math 481: Mathematical Logic

 

Homework 6 due
Weekly Schedule
Week 1
Date Topic Notes Homework
Wed (9/9) Syntax of propositional logic
Fri (9/11) Structural induction and structural recursion Homework 1 (due 9/21)
Solution
Week 2
Date Topic Notes Homework
Mon (9/14) Truth tables and tautologies
Wed (9/16) Truth valuations and tautological consequence
Fri (9/18) Tautological equivalence and the replacement theorems
Week 3
Date Topic Notes Homework
Mon (9/21) Truth functional completeness Homework 1 due
Wed (9/23) Normal forms, uniform notation
Fri (9/25) Beginning proof theory: Semantic Tableaux
Week 4
Date Topic Notes Homework
Mon (9/28) Semantic Tableaux, finite proofs Homework 2 (due 10/7)
solutions
Wed (9/30) Natural deduction proofs
Fri (10/2) Natural deduction proofs
Week 5
Date Topic Notes Homework
Mon (10/5) Natural Deduction continued
Wed (10/7) Soundness and Completeness theorems for Semantic Tableaux
  • notes on Soundness Theorem
  • notes on Completeness Theorem
Homework 2 due
Fri (10/9) Proof from Premises
  • notes proof from premises
Week 6
Date Topic Notes Homework
Mon (10/12) Strong Soundness and Completeness for Semantic Tableaux Homework 3 (due 10/21)
Wed (10/14) Abstract Completness Theorem
Fri (10/16) Craig Interpolation Theorem
Week 7
Date Topic Notes Homework
Mon (10/19) NO CLASS
Wed (10/21) Consequences ofthe Compactness Theorem
Homework 3 due
Fri (10/23) Exam
Week 8
Date Topic Notes Homework
Mon (10/26) Applications of Propositional Compactness
Introduction to First-Order Languages
Wed (10/28) Syntax of First-Order Languages
Fri (10/30) Structural Induction and Recursion
Week 9
Date Topic Notes Homework
Mon (11/2) Structural Induction And Recursion
Wed (11/4) First-order semantics: Truth
Fri (11/6) First-order semantics: validity
Week 10
Date Topic Notes Homework
Mon (11/9) Logical Equivalence
Wed (11/11) Semantic Tableaux
Fri (11/13) Semantic Tableaux Homework 5 (due 11/23)
Week 11
Date Topic Notes Homework
Mon (11/16) Natural Deduction Proofs
Wed (11/18) Natural Deduction Proofs
  • Modern Formal Logic Primer This is a text by Paul Teller (now online) which provides a very good introduction to natural deduction and semantic tableaux for first-order logic. There are some minor differences (we use parameters, where Teller uses variables), but the rules are essentially the same.
Fri (11/20) Hintikka's Lemma
Week 12
Date Topic Notes Homework
Mon (11/23) Exam
solutions
Homework 5 due
Wed (11/25) No Class
Fri (11/27) No Class
Week 13
Date Topic Notes Homework
Mon (11/30) Hintikka's Lemma
Wed (12/2) Soundness and Completeness of Semantic Tableaux
Fri (12/4) Abstract Completeness Theorem
Week 14
Date Topic Notes Homework
Mon (12/7) Soundness and Completeness of System of Natural Deduction
Wed (12/9) Craig Interpolation Theorem
Fri (12/11) Craig Interpolation Theorem
Week 15
Date Topic Notes Homework
Mon (12/14) Beth Definability