Backward Chaining
In backward chaining, if it is desired to prove the conclusion C of a clause, the system tries to do so by proving the premises P1 ... Pn.
∀ x CAR(x) ∧ RED(x) → EXPENSIVE(x)
Given this axiom, an attempt to prove that BMW1 is expensive would be reduced to the subproblems of proving that it is a car and that it is red.
Problems:
∀ x ∀ y ∀ z GREATER(x,y) ∧ GREATER(y,z) → GREATER(x,z)