COMPSCI 513/613: Logic in Computer Science, Fall 2023

Contents: This course is a rigorous introduction to mathematical logic from an algorithmic perspective. Topics include: Propositional logic and SAT solvers; First Order Logic: soundness and completeness of resolution, compactness theorem, automatic theorem proving, model checking. We will learn about and use the Coq theorem prover, Datalog, model checkers, and SAT and SMT solvers. Undergraduate Prerequisites: COMPSCI 250 (discrete math) and COMPSCI 311 (algorithms).

Times: TuTh 8:30-9:45am
Instructor: Marius Minea (marius at cs), office: LGRC A261
Textbook: Uwe Schöning, Logic for Computer Scientists, Birkhäuser, 2008. Available through UMass subscription
Topics:

1. Introduction
2. Propositional Calculus
3. Compactness of Propositional Calculus
4. Resolution for Propositional Calculus
5. First-Order Logic: Syntax and Semantics
6. Prenex Normal Form and the Truth Game
7. Ehrenfeucht-Fraissé Games
8. Skolemization and First-Order Resolution
9. Herbrand's Theorem
10. Unification and Completeness of First-Order Resolution
11. Consequences of Completeness
12. Decidability and Undecidability
13. Undecidability of First-Order Logic and Gödel's Incompleteness Theorem
14. Inductive Definitions, Least Fixed Points, Datalog and Prolog
15. Model Checking. Linear Temporal Logic (LTL)
16. Computation Tree Logic: CTL, CTL*
17. Ordered Binary Decision Diagrams. Symbolic Model Checking
18. SAT Solvers
19. Descriptive Complexity
20. The Alloy Analyzer
21. The Coq Proof Assistant
22. TBD + Project Presentations