This is continuation of lecture06.

Goals:

• discuss proof systems for propositional logic that are useful for SAT solvers
• further illustrate notions of soundness and completeness of proof systems
• show properties of proof systems on infinite formulas, because they will be useful in first-order logic
• discuss some SAT solving techniques

Satisfiability of Sets of Formulas

Compactness Theorem

Definition of Propositional Resolution

Deriving Propositional Resolution

Interpolants from Resolution Proofs

Polynomial Algorithm for Horn Clauses and Boolean Constraint Propagation

Schaefer's dichotomy theorem

Continued in lecture08.

• Calculus of Computation Textbook, Chapter 1
• Logic for Mathematics and Computer Science Textbook
• Gallier Logic Book
• An Introduction to Mathematical Logic and Type Theory
• Course at MPI, Lecture 4
• Ganzinger-Bachmair Model Construction