9 10 points Show how to use Backward Chaining to prove Q Cle

9. (10 points) Show how to use Backward Chaining to prove Q. Clearly show all steps of the proof.

Solution

Answer:-

Backward chaining :

Backward chaining starts with a list of goals (or a hypothesis) and works backwards from the consequent to the antecedent to see if there is data available that will support any of these consequents.

The engine using backward chaining would search the inference rules until it finds one which has a consequent (Then clause) that matches a desired goal. If the antecedent (If clause) of that rule is not known to be true, then it is added to the list of goals (in order for one\'s goal to be confirmed one must also provide data that confirms this new rule).

suppose a new pet, Fritz, is delivered in an opaque box along with two facts about Fritz:

1) Fritz croaks
2) Fritz eats flies

The goal is to decide whether Fritz is green, based on a rule base containing the following four rules:

1) An Example of Backward Chaining.
2) An Example of Backward Chaining.
3) If X croaks and X eats flies – Then X is a frog
4) If X chirps and X sings – Then X is a canary
5) If X is a frog – Then X is green

6) If X is a canary – Then X is yellow

1. Fritz is substituted for X in rule #3 to see if its consequent matches the goal, so rule #3 becomes:

If Fritz is a frog – Then Fritz is green

Since the consequent matches the goal (\"Fritz is green\"),the rules engine now needs to see if the antecedent (\"If Fritz is a frog\") can be proved. The antecedent therefore becomes the new goal:

Fritz is a frog

2. Again substituting Fritz for X, rule #1 becomes:

If Fritz croaks and Fritz eats flies – Then Fritz is a frog
Since the consequent matches the current goal (\"Fritz is a frog\"), the inference engine now needs to see if the antecedent (\"If Fritz croaks and eats flies\") can be proved. The antecedent therefore becomes the new goal:

Fritz croaks and Fritz eats flies

3. Since this goal is a conjunction of two statements, the inference engine breaks it into two sub-goals, both of which must be proved:

Fritz croaks
Fritz eats flies

4. To prove both of these sub-goals, the inference engine sees that both of these sub-goals were given as initial facts. Therefore, the conjunction is true:

Fritz croaks and Fritz eats flies

therefore the antecedent of rule #1 is true and the consequent must be true:

Fritz is a frog
therefore the antecedent of rule #3 is true and the consequent must be true:

Fritz is green