3. Forward Chaining (propositional)

4. Recursive stack-based version of Back-chaining using Propositional Logic
could be modified to handle...
variables (using unification)
negation
context (fail if sub-goal is repeated)
Backchain(KB,query)
stack {query} // initialize
return BC(KB,stack)
BC(KB,stack)
if stack empty, return True
goal  stack.pop()
if goalKB, return BC(KB,stack) // a known fact
for each rule a1..angoal in KB:
stack.push(a1..an)
result  BC(KB,stack)
if result=True, return True
remove a1..an from stack
return False

5. KB = {CanBikeToWork  CanGetToWork
CanDriveToWork  CanGetToWork
CanWalkToWork  CanGetToWork
HaveBike  Sunny  CanBikeToWork
OwnCar  CanDriveToWork
HaveMoney  RentCar  CanDriveToWork
HaveMoney  TaxiAvailable  CanDriveToWork
Sunny  CanWalkToWork
HaveUmbrella  CanWalkToWork
Rainy, // facts
HaveBike,
HaveMoney,
RentCar }
query = CanGetToWork ?

6. {CanGetToWork} // initialize goal stack with query
{CanBikeToWork} // replace subgoal with rule 1
{HaveBike,Sunny} // push antecedents for rule 4
{Sunny} // HaveBike is fact, so pop it
backtrack since Sunny in not a fact and can’t be proved
{CanDriveToWork} // rule 2, another way CanGetToWork
{OwnCar} // try rule 5
backtrack, not provable
{HaveMoney,RentCar} // another way to prove CanDriveToWork
{RentCar} // pop HaveMoney since known fact
{} // success! empty goal stack, return True