CS50 AI - Knights - Knowledge 3

Question

having a little trouble with the last part of the knights challenge. When run, it will print nothing for puzzle 3. I have been through the logic countless times now and in my head it seems to work. Any one know why this is not working as expected? Thanks in advance.

knowledge3 = And(
# Information given in the definition of a Knight and Knave puzzle
# Each character is either a knight or a Knave
Or(AKnight, AKnave),
Or(BKnight, BKnave),
Or(CKnight, CKnave),

# Not both
Biconditional(AKnight, Not(AKnave)),
Biconditional(AKnave, Not(AKnight)),

Biconditional(BKnight, Not(BKnave)),
Biconditional(BKnave, Not(BKnight)),

Biconditional(CKnight, Not(CKnave)),
Biconditional(CKnave, Not(CKnight)),

# Information about what the characters actually said
# A says either "I am a knight." or "I am a knave.", but you don't know which.
Or(Implication(AKnight, AKnight), Implication(AKnight, AKnave)),
Or(Implication(AKnave, Not(AKnight)), Implication(AKnave, Not(AKnave))),

# B says "A said 'I am a knave'."
Implication(BKnight, Or(Implication(AKnight, AKnave), Implication(AKnave, Not(AKnave)))),
Implication(BKnave, Or(Not(Implication(AKnight, AKnave)), Not(Implication(AKnave, Not(AKnave))))),

# B says "C is a knave."
Implication(BKnight, CKnave),
Implication(BKnave, CKnight),

# C says "A is a knight."
Implication(CKnight, AKnight),
Implication(CKnave, AKnave)

)

Answer 1

How did you reason about this statement:

# Information about what the characters actually said
# A says either "I am a knight." or "I am a knave.", but you don't know which.
Or(Implication(AKnight, AKnight), Implication(AKnight, AKnave)),
Or(Implication(AKnave, Not(AKnight)), Implication(AKnave, Not(AKnave))),

It seems to be a problem with the Or() statement, in the AKnave case. You have two implications, that is:
(A->B) or (A->C) . This could be written as A -> (B or C). If A is AKnight, the statement is correct. If A is AKnave, you want to negate the consequent. That is, A-> Not(B or C). You can use DeMorgans's law to move the Not inside the parenthesis . That is, Not(B or C) becomes Not B AND Not C. That is, A -> (not B AND not C) should be used in the AKNave case. If you want to use two implications, just expand it.