Lecture topics (by week) and corresponding reading from the text (in parentheses, updated as lectures progress):

1. Introduction and Brief History, Goals;
   Formal Languages and Syntax of Propositional Logic (Chapter 2: 2.2, 2.3)
2. Propositional Model Theory: Interpretations and Models,
   Logical Implication/Entailment (Chapter 2: (2.1), 2.4, 2.5, 2.8)
3. Proofs in Propositional Logic: The Hilbert System,
   Soundness of the Hilbert System (4.1, 5.1-3 only propositional cases)
4. Completeness of the Hilbert System,
   Compactness and Applications (6.1; summary of definitions and main theorems);
5. Sequent Calculus (handout);
   Basic Modal Systems: Models and Proofs (Chapter 8: on level covered in class)
6. Definability and Correspondence Theory in Modal Logic,
   From Modal Logic to Hoare Triples and Program Verification (summary of definitions and main theorems);
7. First-Order Logic: Syntax and Semantics (Chapter 3: 3.1-4)
   First-Order Logic: Examples and Applications
8. review for midterm
   midterm (no class)
9. Proof Systems for First-Order Logic: Soundness,
   Completeness, and Equality (Chapter 4; Chapter 5: 5.1,2,4,5; Chapter 6: 6.1)
10. Compactness and Definability (6.2; summary of definitions and main theorems);
    Clausal Normal Form and Resolution Proofs (6.3, propositional, first-order),
11. Introduction to Computability: Programs as Formulas,
    Decision Problems, Diagonalization and Self-reference
12. Halting Problem and Reductions,
    review for final