I was given the following text:
If Cleopatra was powerful, then she was venerated but if she was not powerful, then she was not venerated and she was feared. If Cleopatra was either venerated or feared, then she was a queen. Cleopatra was a leader if she was a queen.
P = Cleopatra was Powerful
V = Cleopatra was Venerated
F = Cleopatra was Feared
Q = Cleopatra was a Queen
L = Cleopatra was a Leader
I am being asked if I can prove that Cleopatra was Powerful? A Leader? A Queen? (without using resolution-refutation).
1. P -> V
2. !P -> (!V and F)
3. (V or F) -> Q
4. Q -> L
CNF Format (shouldn’t be needed but incase):
1. ! P or V
2a. (P or !V)
2b. (P or F)
3a. (!V or Q)
3b. (!F or Q)
4. !Q or L
From here I was able, with resolution-refutation, to determine that we cannot prove P but we should be able to prove Q and L… After that I am completely stuck on how to proceed as I am not allowed to prove the question with that approach – only to help me see what answers I should get…
I assume I must either use Forward-Chaining or Backward-Chaining to solve the problems – but no knowledge is given, only implications – so how is one supposed to use either? In all my readings usually we would be given something like F=True (knowledge) or something similar and the chaining would come down to that – but with only implications I can’t see how anything can be proven…
All my attempts (and there have been many) have only added to my confusion.
Any help/hints would be greatly appreciated.