def test_inclusion_revision(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
bb.revise(Belief(phi))
bb2.expand(Belief(phi))
assert bb.beliefs.issubset(bb2.beliefs)
def test_vacuity_revision(self):
bb = self.belief_base
phi = self.p
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
# Phi is not a member of Belief Base
if entails(bb.get_clauses(), Not(phi)):
assert False
bb.revise(Belief(phi))
bb2.expand(Belief(phi))
assert bb == bb2
def test_extensionality_revision(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = Or(self.p, self.q)
xi = Or(self.p, self.q)
# Phi is not a member of Belief Base
if not entails({}, Biconditional(phi, xi)):
assert False
bb.revise(Belief(phi))
bb2.revise(Belief(xi))
assert bb == bb2
def test_extensionality_contraction(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = Implication(self.p, self.q)
xi = Or(Not(self.p), self.q)
# Phi is not a member of Belief Base
if entails({}, Biconditional(phi, xi)):
assert False
bb.contract(Belief(phi))
bb2.contract(Belief(xi))
assert bb == bb2
def test_conjunctive_inclusion_contraction(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
xi = self.q
# Phi is not a member of Belief Base
bb.contract(Belief(And(phi, xi)))
if entails(bb.get_clauses(), phi):
assert False
bb2.contract(Belief(phi))
assert bb.beliefs.issubset(bb2.beliefs)
def test_closure_contraction(self):
"""
The outcome of contraction is logically closed
"""
bb = self.belief_base
bb.contract(Belief(self.p))
clauses = bb.get_clauses()
cn_bb = BeliefBase(selection_function=select_largest_set)
# Check that all formulas in the belief base is a logical consequence of the belief base
for belief in bb.beliefs:
if entails(clauses, belief.formula):
cn_bb.expand(belief)
assert cn_bb == bb
def test_subexpansion_revision(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
xi = self.q
# Phi is not a member of Belief Base
bb.revise(Belief(phi))
if entails(bb.get_clauses(), Not(xi)):
assert False
bb.expand(Belief(xi))
bb2.revise(Belief(And(phi, xi)))
assert bb.beliefs.issubset(bb2.beliefs)
def test_recovery_contraction(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
bb.contract(Belief(phi))
bb.expand(Belief(phi))
assert bb.beliefs.issubset(bb2.beliefs)
def test_conjunctive_overlap_contraction(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
bb3 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
xi = self.q
# Phi is not a member of Belief Base
bb.contract(Belief(xi))
bb2.contract(Belief(phi))
bb3.contract(Belief(And(xi, phi)))
assert bb.beliefs.intersection(bb2.beliefs).issubset(bb3.beliefs)
def test_superexpansion_revision(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
xi = self.q
# Phi is not a member of Belief Base
bb.revise(Belief(And(phi, xi)))
bb2.revise(Belief(phi))
bb2.expand(Belief(xi))
assert bb.beliefs.issubset(bb2.beliefs)
class TestAGMPostulates(TestCase):
belief_base = BeliefBase(selection_function=select_largest_set)
p = Proposition("p")
q = Proposition("q")
def setUp(self) -> None:
self.belief_base.clear()
bb: BeliefBase = self.belief_base
p = self.p
q = self.q
bb.expand(Belief(p))
bb.expand(Belief(q))
bb.expand(Belief(And(p, q)))
bb.expand(Belief(Or(p, q)))
bb.expand(Belief(Implication(p, q)))
self.belief_base = bb
def test_closure_revision(self):
"""
The outcome of revision is logically closed
"""
bb = self.belief_base
bb.revise(Belief(self.p))
clauses = bb.get_clauses()
cn_bb = BeliefBase(selection_function=select_largest_set)
# Check that all formulas in the belief base is a logical consequence of the belief base
for belief in bb.beliefs:
if entails(clauses, belief.formula):
cn_bb.expand(belief)
assert cn_bb == bb
def test_closure_contraction(self):
"""
The outcome of contraction is logically closed
"""
bb = self.belief_base
bb.contract(Belief(self.p))
clauses = bb.get_clauses()
cn_bb = BeliefBase(selection_function=select_largest_set)
# Check that all formulas in the belief base is a logical consequence of the belief base
for belief in bb.beliefs:
if entails(clauses, belief.formula):
cn_bb.expand(belief)
assert cn_bb == bb
def test_success_contraction(self):
bb = self.belief_base
phi = self.p
# Phi is not a tautology
if entails({}, phi):
assert False
bb.contract(Belief(phi))
assert not entails(bb.get_clauses(), phi)
def test_success_revision(self):
bb = self.belief_base
phi = self.p
bb.revise(Belief(phi))
assert entails(bb.get_clauses(), phi)
def test_inclusion_contraction(self):
bb = self.belief_base
phi = self.p
# Phi is not a tautology
if entails({}, phi):
assert False
bb.revise(Belief(phi))
assert entails(bb.get_clauses(), phi)
def test_inclusion_revision(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
bb.revise(Belief(phi))
bb2.expand(Belief(phi))
assert bb.beliefs.issubset(bb2.beliefs)
def test_vacuity_contraction(self):
bb = self.belief_base
phi = Proposition("r")
# Phi is not a member of Belief Base
if entails(bb.get_clauses(), phi):
assert False
bb.contract(Belief(phi))
assert bb == bb
def test_vacuity_revision(self):
bb = self.belief_base
phi = self.p
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
# Phi is not a member of Belief Base
if entails(bb.get_clauses(), Not(phi)):
assert False
bb.revise(Belief(phi))
bb2.expand(Belief(phi))
assert bb == bb2
def test_extensionality_contraction(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = Implication(self.p, self.q)
xi = Or(Not(self.p), self.q)
# Phi is not a member of Belief Base
if entails({}, Biconditional(phi, xi)):
assert False
bb.contract(Belief(phi))
bb2.contract(Belief(xi))
assert bb == bb2
def test_extensionality_revision(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = Or(self.p, self.q)
xi = Or(self.p, self.q)
# Phi is not a member of Belief Base
if not entails({}, Biconditional(phi, xi)):
assert False
bb.revise(Belief(phi))
bb2.revise(Belief(xi))
assert bb == bb2
def test_recovery_contraction(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
bb.contract(Belief(phi))
bb.expand(Belief(phi))
assert bb.beliefs.issubset(bb2.beliefs)
def test_conjunctive_inclusion_contraction(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
xi = self.q
# Phi is not a member of Belief Base
bb.contract(Belief(And(phi, xi)))
if entails(bb.get_clauses(), phi):
assert False
bb2.contract(Belief(phi))
assert bb.beliefs.issubset(bb2.beliefs)
def test_conjunctive_overlap_contraction(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
bb3 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
xi = self.q
# Phi is not a member of Belief Base
bb.contract(Belief(xi))
bb2.contract(Belief(phi))
bb3.contract(Belief(And(xi, phi)))
assert bb.beliefs.intersection(bb2.beliefs).issubset(bb3.beliefs)
def test_superexpansion_revision(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
xi = self.q
# Phi is not a member of Belief Base
bb.revise(Belief(And(phi, xi)))
bb2.revise(Belief(phi))
bb2.expand(Belief(xi))
assert bb.beliefs.issubset(bb2.beliefs)
def test_subexpansion_revision(self):
bb = self.belief_base
bb2 = BeliefBase(self.belief_base.beliefs,
selection_function=select_largest_set)
phi = self.p
xi = self.q
# Phi is not a member of Belief Base
bb.revise(Belief(phi))
if entails(bb.get_clauses(), Not(xi)):
assert False
bb.expand(Belief(xi))
bb2.revise(Belief(And(phi, xi)))
assert bb.beliefs.issubset(bb2.beliefs)
class TestBeliefBase(TestCase):
belief_base = BeliefBase(selection_function=select_largest_set)
p = Proposition("p")
q = Proposition("q")
r = Proposition("r")
def setUp(self) -> None:
self.belief_base.clear()
def test_remainder(self):
"""
Test remainders for KB:
{p, q, p ∧ q, p ∨ q, p → q}
Contract formula:
q
Resulting remainders:
{{p, p ∨ q}, {p → q}}
"""
bb = self.belief_base
p = self.p
q = self.q
bb.expand(Belief(p))
bb.expand(Belief(q))
bb.expand(Belief(And(p, q)))
bb.expand(Belief(Or(p, q)))
bb.expand(Belief(Implication(p, q)))
remainders = bb._get_remainders(Belief(q))
assert remainders == [{Belief(p), Belief(Or(p, q))},
{Belief(Implication(p, q))}]
def test_contraction(self):
"""
Selection function selects only the largest set
Test contraction for KB:
{p, q, p ∧ q, p ∨ q, p → q}
Contract formula:
q
Resulting best set:
{p, p ∨ q}
"""
bb = self.belief_base
p = self.p
q = self.q
bb.expand(Belief(p))
bb.expand(Belief(q))
bb.expand(Belief(And(p, q)))
bb.expand(Belief(Or(p, q)))
bb.expand(Belief(Implication(p, q)))
bb.contract(Belief(q))
assert bb.beliefs == {Belief(p), Belief(Or(p, q))}
def test_revision(self):
"""
Test revision for KB:
{p → q}
Revise formula:
p
Resulting best set:
{p, p -> q}
"""
bb = self.belief_base
p = self.p
q = self.q
bb.expand(Belief(Implication(p, q)))
bb.revise(Belief(p))
assert bb.beliefs == {Belief(p), Belief(Implication(p, q))}