LARA

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Propositional Proofs

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 basic SAT solving algorithms

Satisfiability of Sets of Formulas

Compactness Theorem

Definition of Propositional Resolution

Deriving Propositional Resolution

Interpolants from Resolution Proofs

Polynomial Algorithm for Horn Clauses

DPLL Algorithm for SAT

Continued in lecture08.

References