def test_exercise43(self):
bsays = "b <=> (a <=> ~a)"
csays = "c <=> ~b"
kb = "(%s) /\\ (%s) " % (bsays, csays)
self.assertFalse(Eval.entails(kb, "a"))
self.assertFalse(Eval.entails(kb, "~a"))
self.assertFalse(Eval.entails(kb, "b"))
self.assertTrue(Eval.entails(kb, "~b"))
self.assertTrue(Eval.entails(kb, "c"))
self.assertFalse(Eval.entails(kb, "~c"))
def main():
# Problem 4.1.
print('''
Problem 4.1. Use the function entails to check whether the following
entailment is true or not.
1. False |= True
2. True |= False
3. (A ∧ B) |= (A ⇔ B)
4. (A ⇔ B) |= A ∨ B
5. (A ⇔ B) |= ¬A ∨ B
Solutions:
1. %s
2. %s
3. %s
4. %s
5. %s
''' % (
Eval.entails("False", "True"), # 1. False |= True
Eval.entails("True", "False"), # 2. True |= False
Eval.entails("a /\\ b", "a <=> b"), # 3. (A ∧ B) |= (A ⇔ B)
Eval.entails("a <=> b", "a \\/ b"), # 4. (A ⇔ B) |= A ∨ B
Eval.entails("a <=> b", "~a \\/ b") # 5. (A ⇔ B) |= ¬A ∨ B
))
# Problem 4.2.2
f1 = "Smoke => Smoke"
f2 = "(Smoke => Fire) => (~Smoke => ~Fire)"
f3 = "Smoke \\/ Fire\\/ ~Fire"
f4 = "(Fire => Smoke) /\\ Fire /\\ ~Smoke"
print(
'''
Problem 4.2.2 Use the function tautology, satisfiable, unsatisfiable
to check whether the following formulae is tautology, satisfiable, or unsat-
isfiable. Compare the output with the result from your pencil-and-paper
derivation.
1. Smoke ⇒ Smoke
2. (Smoke ⇒ Fire) ⇒ (¬Smoke ⇒ ¬Fire)
3. Smoke ∨ Fire ∨ ¬Fire
4. (Fire ⇒ Smoke) ∧ Fire ∧ ¬Smoke
Solutions:
1. %s
2. %s
3. %s
4. %s
''' % (
ex42(f1),
ex42(f2),
ex42(f3),
ex42(f4)
))
# Exercise 4.2.3
bsays = "b <=> (a <=> ~a)"
csays = "c <=> ~b"
kb = "(%s) /\\ (%s) " % (bsays, csays)
print(
'''
Problem 4.2.3
Represent what B says with your parser.
bsays = parse "b <=> (a <=> ~a)"
where parse is your parser implementation. Do the same with what C says.
csays = parse "c <=> ~b"
Construct a knowledge base —kb of type Formula— by performing conjunc-
tion of what B and C says. By using the function entails, check whether
the knowledge base entails whether A is a knight. Check also whether it
entails whether A is a knave. Perform these checks for B and C as well.
Solutions:
%s
%s
%s
%s
%s
%s
'''
% (
"KB |= a = " + str(Eval.entails(kb, "a")),
"KB |= ~a = " + str(Eval.entails(kb, "~a")),
"KB |= b = " + str(Eval.entails(kb, "b")),
"KB |= ~b = " + str(Eval.entails(kb, "~b")),
"KB |= c = " + str(Eval.entails(kb, "c")),
"KB |= ~c = " + str(Eval.entails(kb, "~c"))
))
print("size: %d" % Eval.num_valid_valuations(
"((S \\/ ~A) /\\ (~N \\/ ~T \\/ A) /\\ (~C \\/ L \\/ A) /\\ (~U \\/ ~S) /\\ (E))"))
def test_exercise41(self):
self.assertTrue(Eval.entails("False", "True"))
self.assertFalse(Eval.entails("True", "False"))
self.assertTrue(Eval.entails("a /\\ b", "a <=> b"))
self.assertFalse(Eval.entails("a <=> b", "a \\/ b"))
self.assertTrue(Eval.entails("a <=> b", "~a \\/ b"))
