def test_valid():
A, B, C = symbols('A,B,C')
assert valid(A >> (B >> A)) is True
assert valid((A >> (B >> C)) >> ((A >> B) >> (A >> C))) is True
assert valid((~B >> ~A) >> (A >> B)) is True
assert valid(A | B | C) is False
assert valid(A >> B) is False
def test_valid():
A, B, C = symbols('A,B,C')
assert valid(A >> (B >> A)) is True
assert valid((A >> (B >> C)) >> ((A >> B) >> (A >> C))) is True
assert valid((~B >> ~A) >> (A >> B)) is True
assert valid(A | B | C) is False
assert valid(A >> B) is False
def domination_relations(rules):
#print("Calculating Domination Relations______________________________________________________________________________\n")
dominations = set()
for k1, r1 in rules.items(
): #and compare each rule with each of the others
for k2, r2 in rules.items():
#The following simply applies the definition of rule domination to the extensions of the rules in each world
#First check for "improper" domination
if not r1.body and not r2.body:
#(str(r1.body).isspace() or str(r2.body).isspace() ):
continue
#if str(r1.body).isspace():
if not r1.body: #To process rules without conditions
continue
elif not r2.body: # If r2 does not have a body will generally be dominated by r1 when the two heads collide
#str(r2.body).isspace():
#print("r1head: %s" %(r1.head))
#print("r2head: %s" % (r2.head))
r1h_cnf = to_cnf(r1.head)
r2h_cnf = to_cnf(r2.head)
temp3 = And(r1h_cnf, r2h_cnf)
notbothheads = Not(temp3)
if valid(notbothheads) == True:
r2.dominatedBy.add(r1)
else:
r1b_cnf = to_cnf(
r1.body) #convert formulats to CNF for SAT solving
# print(r2.body)
r2b_cnf = to_cnf(r2.body)
r1h_cnf = to_cnf(r1.head)
r2h_cnf = to_cnf(r2.head)
temp1 = Not(
r1.body
) #putting together formulas for testing the domination condition
temp2 = Not(r2.body)
r1b_r2b = Or(temp1, r2b_cnf)
r2b_r1b = Or(temp2, r1b_cnf)
temp3 = And(r1h_cnf, r2h_cnf)
notbothheads = Not(temp3)
#print("First: %s, %s \n" % (r1b_r2b, notbothheads) )
if ((valid(r1b_r2b) == True) and valid(notbothheads) == True):
if (valid(r2b_r1b) == False
or valid(notbothheads) == False):
new = (r1.name, r2.name)
dominations.add(new)
if (r2.item != r1.item):
r2.dominatedBy.add(r1)
def eval(variable, expr):
if valid(expr) == True:
return true
return Forall(variable, expr, evaluate=False)