Business rules systems and logic programming are definitely similar. Most business rules are based on "Forward Chaining" (https://en.wikipedia.org/wiki/Forward_chaining), basically using what we know to satisfy the left hand side condition and then using the right hand side to assert new facts. Logic programming is usually based on "Backward Chaining" (https://en.wikipedia.org/wiki/Backward_chaining), where the system attempts to work backwards from a goal to what facts are needed to satisfy the goal.