def axioms(features, labels, training=False):
x_A = ltn.Variable("x_A",features[labels==0])
x_B = ltn.Variable("x_B",features[labels==1])
x_C = ltn.Variable("x_C",features[labels==2])
axioms = [
Forall(x_A,p([x_A,class_A],training=training)),
Forall(x_B,p([x_B,class_B],training=training)),
Forall(x_C,p([x_C,class_C],training=training))
]
sat_level = formula_aggregator(axioms).tensor
return sat_level
def axioms(images_x, images_y, labels_z, p_schedule=tf.constant(2.)):
images_x = ltn.Variable("x", images_x)
images_y = ltn.Variable("y", images_y)
labels_z = ltn.Variable("z", labels_z)
axiom = Forall(
ltn.diag(images_x,images_y,labels_z),
Exists(
(d1,d2),
And(Digit([images_x,d1]),Digit([images_y,d2])),
mask=equals([add([d1,d2]), labels_z]),
p=p_schedule
),
p=2
)
sat = axiom.tensor
return sat
def axioms(features, labels_sex, labels_color):
x = ltn.Variable("x", features)
x_blue = ltn.Variable("x_blue", features[labels_color == "B"])
x_orange = ltn.Variable("x_orange", features[labels_color == "O"])
x_male = ltn.Variable("x_blue", features[labels_sex == "M"])
x_female = ltn.Variable("x_blue", features[labels_sex == "F"])
axioms = [
Forall(x_blue, p([x_blue, class_blue])),
Forall(x_orange, p([x_orange, class_orange])),
Forall(x_male, p([x_male, class_male])),
Forall(x_female, p([x_female, class_female])),
Forall(x, Not(And(p([x, class_blue]), p([x, class_orange])))),
Forall(x, Not(And(p([x, class_male]), p([x, class_female]))))
]
sat_level = formula_aggregator(axioms).tensor
return sat_level
def axioms(images_x1, images_x2, images_y1, images_y2, labels_z, p_schedule):
images_x1 = ltn.Variable("x1", images_x1)
images_x2 = ltn.Variable("x2", images_x2)
images_y1 = ltn.Variable("y1", images_y1)
images_y2 = ltn.Variable("y2", images_y2)
labels_z = ltn.Variable("z", labels_z)
axiom = Forall(
ltn.diag(images_x1, images_x2, images_y1, images_y2, labels_z),
Exists(
(d1, d2, d3, d4),
And(And(Digit([images_x1, d1]), Digit([images_x2, d2])),
And(Digit([images_y1, d3]), Digit([images_y2, d4]))),
mask=equals([
labels_z,
add([two_digit_number([d1, d2]),
two_digit_number([d3, d4])])
]),
p=p_schedule),
p=2)
sat = axiom.tensor
return sat
def axioms(data, labels):
x_A = ltn.Variable("x_A", data[labels])
x_not_A = ltn.Variable("x_not_A", data[tf.logical_not(labels)])
axioms = [Forall(x_A, A(x_A)), Forall(x_not_A, Not(A(x_not_A)))]
sat_level = formula_aggregator(axioms).tensor
return sat_level
def axioms(x_data, y_data):
x = ltn.Variable("x", x_data)
y = ltn.Variable("y", y_data)
return Forall(ltn.diag(x,y), eq([f(x),y]))
""" DATASET """
ds_train, ds_test = data.get_mnist_op_dataset(
count_train=n_examples_train,
count_test=n_examples_test,
buffer_size=10000,
batch_size=batch_size,
n_operands=2,
op=lambda args: args[0]+args[1])
""" LTN MODEL AND LOSS """
### Predicates
logits_model = baselines.SingleDigit()
Digit = ltn.Predicate(ltn.utils.LogitsToPredicateModel(logits_model))
### Variables
d1 = ltn.Variable("digits1", range(10))
d2 = ltn.Variable("digits2", range(10))
### Operators
Not = ltn.Wrapper_Connective(ltn.fuzzy_ops.Not_Std())
And = ltn.Wrapper_Connective(ltn.fuzzy_ops.And_Prod())
Or = ltn.Wrapper_Connective(ltn.fuzzy_ops.Or_ProbSum())
Implies = ltn.Wrapper_Connective(ltn.fuzzy_ops.Implies_Reichenbach())
Forall = ltn.Wrapper_Quantifier(ltn.fuzzy_ops.Aggreg_pMeanError(),semantics="forall")
Exists = ltn.Wrapper_Quantifier(ltn.fuzzy_ops.Aggreg_pMean(),semantics="exists")
# mask
add = ltn.Function.Lambda(lambda inputs: inputs[0]+inputs[1])
equals = ltn.Predicate.Lambda(lambda inputs: inputs[0] == inputs[1])
### Axioms
def sat_phi3(features):
x = ltn.Variable("x", features)
phi3 = Forall(x, Implies(p([x, class_blue]), p([x, class_male])), p=5)
return phi3.tensor
def sat_phi2(features):
x = ltn.Variable("x", features)
phi2 = Forall(x, Implies(p([x, class_blue]), p([x, class_orange])), p=5)
return phi2.tensor
p_type = args["p"]
""" DATASET """
ds_train, ds_test = data.get_mnist_op_dataset(
count_train=n_examples_train,
count_test=n_examples_test,
buffer_size=10000,
batch_size=batch_size,
n_operands=4,
op=lambda args: 10 * args[0] + args[1] + 10 * args[2] + args[3])
""" LTN MODEL AND LOSS """
### Predicates
logits_model = baselines.SingleDigit()
Digit = ltn.Predicate(ltn.utils.LogitsToPredicateModel(logits_model))
### Variables
d1 = ltn.Variable("digits1", range(10))
d2 = ltn.Variable("digits2", range(10))
d3 = ltn.Variable("digits3", range(10))
d4 = ltn.Variable("digits4", range(10))
### Operators
Not = ltn.Wrapper_Connective(ltn.fuzzy_ops.Not_Std())
And = ltn.Wrapper_Connective(ltn.fuzzy_ops.And_Prod())
Or = ltn.Wrapper_Connective(ltn.fuzzy_ops.Or_ProbSum())
Implies = ltn.Wrapper_Connective(ltn.fuzzy_ops.Implies_Reichenbach())
Forall = ltn.Wrapper_Quantifier(ltn.fuzzy_ops.Aggreg_pMeanError(),
semantics="forall")
Exists = ltn.Wrapper_Quantifier(ltn.fuzzy_ops.Aggreg_pMean(),
semantics="exists")
# mask
add = ltn.Function.Lambda(lambda inputs: inputs[0] + inputs[1])
