Backward Chaining

Suppose that we have formulas:
A
B
D
A ∧ B → C or C ← A ∧ B
C ∧ D → E or E ← C ∧ D

A conclusion E can be proved recursively:

1. First check whether the desired conclusion is in the database of facts. If so, return True.

2. Otherwise, for each rule that has the desired conclusion as its right-hand side, call the algorithm recursively for each item in the premise (left-hand side). If all of the premises are true, return True.

3. Otherwise, return False.

In this example, we would know that E is true if we knew that C and D were true; we would know that C is true if we knew A and B ; A and B are in the database, so C must be true; and D is in the database, so E is true.