Conjunctive Normal Form

For a resolution program, we want to eliminate as much of the logic notation as possible. This is done in the following ways:

• Universal ∀ quantifiers are eliminated by assuming that any variable is universally quantified: x .

• Existential ∃ quantifiers are eliminated by Skolemizing and turning existential variables into constants, which are functions of no arguments: (b) .

• Predicates in a clause are assumed to be connected by ∨ .

• Clauses are assumed to be connected by ∧ .

• The only operator remaining is not

• The conclusion is negated and added to the set of clauses.

A clause such as ``all hounds howl'' becomes:
∀ x Hound(x) → Howl(x)
¬ Hound(x) ∨ Howl(x)
( (not (hound x)) (howl x) )