Resolution
- Resolution is a sound and complete inference procedure for FOL.
- Resolution uses a single rule of inference: the Resolution Rule,
which is a generalization of the same rule used in PL.
- Resolution Rule for PL:
From sentence P1 v P2 v ... v Pn and sentence ~P1 v Q2 v ... v Qm
derive resolvent sentence: P2 v ... v Pn v Q2 v ... v Qm
- Examples
- From P and ~P v Q, derive Q (Modus Ponens)
- From (~P v Q) and (~Q v R), derive ~P v R
- From P and ~P, derive False
- From (P v Q) and (~P v ~Q), derive True
- Proof is by contradiction.