def testSimplePredicateOptimization(self):
nr_samples=100
ltnw.variable("?data_A",numpy.random.uniform([0.,0.],[.1,1.],(nr_samples,2)).astype("float32"))
ltnw.variable("?data_not_A",numpy.random.uniform([2.,0],[3.,1.],(nr_samples,2)).astype("float32"))
ltnw.predicate("A",2)
ltnw.axiom("forall ?data_A: A(?data_A)")
ltnw.axiom("forall ?data_not_A: ~A(?data_not_A)")
ltnw.initialize_knowledgebase(initial_sat_level_threshold=.1)
sat_level=ltnw.train(track_sat_levels=10000,sat_level_epsilon=.99)
self.assertGreater(sat_level,.8)
ltnw.constant("a",[0.5,0.5])
ltnw.constant("b",[2.5,0.5])
self.assertGreater(ltnw.ask("A(a)")[0],.8)
self.assertGreater(ltnw.ask("~A(b)")[0],.8)
result=ltnw.ask_m(["A(a)","~A(b)"])
for r in result:
self.assertGreater(r[0],.8)
self.assertGreater(r[0],.8)
def testSimplePredicate(self):
import tensorflow
nr_samples=100
ltnw.constant("a",[2.,3.])
ltnw.variable("?data_A",numpy.random.uniform([0.,0.],[.1,1.],(nr_samples,2)).astype("float32"))
mu=tensorflow.constant([2.,3.])
ltnw.predicate("A",2,pred_definition=lambda x: tensorflow.exp(-tensorflow.norm(tensorflow.subtract(x,mu),axis=1)));
self.assertEqual(ltnw.ask("A(a)"),1.)
self.assertGreater(ltnw.ask("forall ?data_A: A(?data_A)"),0.)
def testBuildFormula(self):
data = numpy.random.uniform([-1,-1],[1,1],(500,2),).astype(numpy.float32)
ltnw.constant("c",[1.,0])
ltnw.variable("?var",data)
ltnw.variable("?var2",data)
ltnw.function("f",2,fun_definition=lambda d:d[:,:2])
ltnw.function("g",4,fun_definition=lambda d:d)
ltnw.predicate("P",2)
ltnw.predicate("B",2)
ltnw.predicate("REL",4)
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("P(c)")))
with self.assertRaises(Exception):
ltnw._build_formula(ltnw._parse_formula("P(d)"))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("P(?var)")))
with self.assertRaises(Exception):
ltnw._build_formula(ltnw._parse_formula("P(?vars)"))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("P(f(?var))")))
with self.assertRaises(Exception):
ltnw._build_formula(ltnw._parse_formula("P(h(?var))")) # h not declared
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("~P(?var)")))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("~P(f(?var))")))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("~REL(?var,?var2)")))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("~REL(?var,f(g(?var2)))")))
with self.assertRaises(Exception):
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("~REL(f(?var))")))
for op in ["&","|","->"]:
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("P(?var) %s ~ P(?var)" % op)))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("P(?var) %s ~ P(?var)" % op)))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("~P(?var) %s P(?var)" % op)))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("~P(?var) %s ~P(?var)" % op)))
for i in range(10):
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("P(?var) %s ~P(?var)%s ~P(?var)%s P(?var)" % tuple(numpy.random.permutation(["&","|","->"])))))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("forall ?var: P(?var) & ~ P(?var)")))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("forall ?var,?var2: P(?var) & ~ P(?var2)")))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("P(c) & (forall ?var,?var2: P(?var) & ~ P(?var2))")))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("exists ?var: P(?var) & ~ P(?var)")))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("exists ?var,?var2: P(?var) & ~ P(?var2)")))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("forall ?var: (exists ?var2: P(?var) & ~ P(?var2))")))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("forall ?var: (exists ?var2: P(?var) & ~ P(?var2))")))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("(forall ?var: (exists ?var2: (P(?var) & P(?var2) & (forall ?var: P(?var)))))")))
self.assertIsNotNone(ltnw._build_formula(ltnw._parse_formula("P(c) | P(?var)")))
# define data
train_X = np.random.uniform(start, end, (training_size)).astype("float32")
train_Y = slope * train_X + np.random.normal(scale=var, size=len(train_X))
# define the language, we translate every training example into constants
[ltnw.constant("x_%s" % i, [x]) for i, x in enumerate(train_X)]
[ltnw.constant("y_%s" % i, [y]) for i, y in enumerate(train_Y)]
# define the function f as a linear regressor
W = tf.Variable(np.random.randn(), name="weight")
b = tf.Variable(np.random.randn(), name="bias")
ltnw.function("f", 1, 1, fun_definition=lambda X: tf.add(tf.multiply(X, W), b))
# defining an equal predicate based on the euclidian distance of two vectors
ltnw.predicate("eq", 2, ltnl.equal_euclidian)
# defining the theory
for f in ["eq(f(x_%s),y_%s)" % (i, i) for i in range(len(train_X))]:
ltnw.axiom(f)
print("\n".join(sorted(ltnw.AXIOMS.keys())))
# initializing knowledgebase and optimizing
ltnw.initialize_knowledgebase(optimizer=tf.train.GradientDescentOptimizer(
learning_rate=learning_rate))
ltnw.train(max_epochs=epochs)
# visualize results on training data
ltnw.variable("?x", 1)
prediction = ltnw.ask("f(?x)",
feed_dict={"?x": train_X.reshape(len(train_X), 1)})
if np.sum(np.square(data[i] - data[j])) < np.square(.5)
])
close_data = close_data[np.random.random_integers(0, len(data), 1000)]
distant_data = np.array([
np.concatenate([data[i], data[j]]) for i in range(len(data))
for j in range(len(data))
if np.sum(np.square(data[i] - data[j])) > np.square(1.)
])
# defining the language
ltnw.variable("?x", data)
ltnw.variable("?y", data)
ltnw.variable("?close_x_y", close_data)
ltnw.variable("?distant_x_y", distant_data)
[ltnw.predicate("C_" + str(i), 2) for i in range(nr_of_clusters)]
ltnw.function("first", 2, fun_definition=lambda d: d[:, :2])
ltnw.function("second", 2, fun_definition=lambda d: d[:, 2:])
print("defining the theory T")
ltnw.axiom("forall ?x: %s" %
"|".join(["C_%s(?x)" % i for i in range(nr_of_clusters)]))
for i in range(nr_of_clusters):
ltnw.axiom("exists ?x: C_%s(?x)" % i)
ltnw.axiom(
"forall ?close_x_y: C_%s(first(?close_x_y)) %% C_%s(second(?close_x_y))"
% (i, i))
ltnw.axiom(
"forall ?distant_x_y: C_%s(first(?distant_x_y)) %% C_%s(second(?distant_x_y))"
% (i, i))
nr_of_points_x_cluster = 50
clusters = []
for i in range(nr_of_clusters):
mean = np.random.uniform([-1, -1], [1, 1], 2).astype(np.float32)
cov = np.array([[.001, 0], [0, .001]])
clusters.append(
np.random.multivariate_normal(mean=mean,
cov=cov,
size=nr_of_points_x_cluster).astype(
np.float32))
data = np.concatenate(clusters)
# define the language
ltnw.variable("?x", data)
ltnw.variable("?y", data)
ltnw.predicate("close", 2, ltnl.equal_euclidian)
[ltnw.predicate("C_" + str(i), 2) for i in range(nr_of_clusters)]
## define the theory
print("defining the theory T")
ltnw.axiom("forall ?x: %s" %
"|".join(["C_%s(?x)" % i for i in range(nr_of_clusters)]))
for i in range(nr_of_clusters):
ltnw.axiom("exists ?x: C_%s(?x)" % i)
ltnw.axiom("forall ?x,?y: (C_%s(?x) & close(?x,?y)) -> C_%s(?y)" % (i, i))
ltnw.axiom(
"forall ?x,?y: (C_%s(?x) & ~close(?x,?y)) -> (%s)" %
(i, "|".join(["C_%s(?y)" % j
for j in range(nr_of_clusters) if i != j])))
for j in range(i + 1, nr_of_clusters):
import numpy as np
import matplotlib.pyplot as plt
import logictensornetworks_wrapper as ltnw
nr_samples=500
data=np.random.uniform([0,0],[1.,1.],(nr_samples,2)).astype(np.float32)
data_A=data[np.where(np.sum(np.square(data-[.5,.5]),axis=1)<.09)]
data_not_A=data[np.where(np.sum(np.square(data-[.5,.5]),axis=1)>=.09)]
ltnw.variable("?data_A",data_A)
ltnw.variable("?data_not_A",data_not_A)
ltnw.variable("?data",data)
ltnw.predicate("A",2)
ltnw.axiom("forall ?data_A: A(?data_A)")
ltnw.axiom("forall ?data_not_A: ~A(?data_not_A)")
ltnw.initialize_knowledgebase(initial_sat_level_threshold=.1)
sat_level=ltnw.train(track_sat_levels=1000,sat_level_epsilon=.99)
plt.figure(figsize=(12,8))
result=ltnw.ask("A(?data)")
plt.subplot(2,2,1)
plt.scatter(data[:,0],data[:,1],c=result.squeeze())
plt.colorbar()
plt.title("A(x) - training data")
result=ltnw.ask("~A(?data)")
logger.basicConfig = logging.basicConfig(level=logging.DEBUG)
import tensorflow as tf
import matplotlib.pyplot as plt
import numpy as np
import logictensornetworks_wrapper as ltnw
import spatial_relations_data
# generate artificial data
nr_examples = 50 # positive and negative examples for each predicate
nr_test_examples=400
# 1) define the language and examples
ltnw.predicate("Left",8)
ltnw.variable("?left_xy",8)
ltnw.variable("?not_left_xy", 8)
ltnw.axiom("forall ?left_xy: Left(?left_xy)")
ltnw.axiom("forall ?not_left_xy: ~Left(?not_left_xy)")
ltnw.predicate("Right",8)
ltnw.variable("?right_xy",8)
ltnw.variable("?not_right_xy",8)
ltnw.axiom("forall ?right_xy: Right(?right_xy)")
ltnw.axiom("forall ?not_right_xy: ~Right(?not_right_xy)")
ltnw.predicate("Below",8)
ltnw.variable("?below_xy",8)
ltnw.variable("?not_below_xy",8)
ltnw.variable('?left_pair',
[full_obj_set[p[0]] + full_obj_set[p[1]] for p in left_pairs])
ltnw.variable('?front_pair',
[full_obj_set[p[0]] + full_obj_set[p[1]] for p in front_pairs])
ltnw.variable('?behind_pair',
[full_obj_set[p[0]] + full_obj_set[p[1]] for p in behind_pairs])
time_diff = time.time() - start_time
print('Time to complete : ', time_diff)
start_time = time.time()
print('******* Predicate/Axioms for Object Features ******')
# Object Features
for feat in obj_feat:
ltnw.predicate(label=feat.capitalize(),
number_of_features_or_vars=num_of_features,
layers=num_of_layers)
for i, feat in enumerate(obj_feat):
ltnw.axiom('forall ?is_' + feat + ' : ' + feat.capitalize() + '(?is_' +
feat + ')')
ltnw.axiom('forall ?isnot_' + feat + ' : ~' + feat.capitalize() +
'(?isnot_' + feat + ')')
# Implicit axioms about object features
## objects can only be one color
for c in obj_colors:
is_color = ''
is_not_color = ''
for not_c in obj_colors:
if not_c == c: is_color = c.capitalize() + '(?obj)'
for l in 'abcdefghijklmn':
ltnw.constant(l,
min_value=[0.] * embedding_size,
max_value=[1.] * embedding_size)
# create variables that ranges on all the individuals, and the individuals of group 1 and group 2.
ltnw.variable("p", tf.concat(list(ltnw.CONSTANTS.values()), axis=0))
ltnw.variable("q", ltnw.VARIABLES["p"])
ltnw.variable("p1", tf.concat([ltnw.CONSTANTS[l] for l in "abcdefgh"], axis=0))
ltnw.variable("q1", ltnw.VARIABLES["p1"])
ltnw.variable("p2", tf.concat([ltnw.CONSTANTS[l] for l in "ijklmn"], axis=0))
ltnw.variable("q2", ltnw.VARIABLES["p2"])
# declare the predicates
ltnw.predicate('Friends', embedding_size * 2)
ltnw.predicate('Smokes', embedding_size)
ltnw.predicate('Cancer', embedding_size)
# add the assertional knowledge in our posses
ltnw.axiom("Friends(a,b)")
ltnw.axiom("~Friends(a,c)")
ltnw.axiom("~Friends(a,d)")
ltnw.axiom("Friends(a,e)")
ltnw.axiom("Friends(a,f)")
ltnw.axiom("Friends(a,g)")
ltnw.axiom("~Friends(a,h)")
ltnw.axiom("Friends(b,c)")
ltnw.axiom("~Friends(b,d)")
ltnw.axiom("~Friends(b,e)")
nr_samples=5
epochs=10000
data_A=np.random.uniform([0,0],[.25,1.],(nr_samples,2)).astype(np.float32)
data_B=np.random.uniform([.75,0],[1.,1.],(nr_samples,2)).astype(np.float32)
data=np.concatenate([data_A,data_B])
ltnw.variable("?data_A",data_A)
ltnw.variable("?data_A_2",data_A)
ltnw.variable("?data_B",data_B)
ltnw.variable("?data_B_2",data_B)
ltnw.variable("?data",data)
ltnw.variable("?data_1",data)
ltnw.variable("?data_2",data)
ltnw.predicate("A",2)
ltnw.predicate("B",2)
ltnw.axiom("forall ?data_A: A(?data_A)")
ltnw.axiom("forall ?data_B: ~A(?data_B)")
ltnw.axiom("forall ?data_B: B(?data_B)")
ltnw.axiom("forall ?data_A: ~B(?data_A)")
ltnw.predicate("R_A_A",4)
ltnw.predicate("R_B_B",4)
ltnw.predicate("R_A_B",4)
ltnw.axiom("forall ?data, ?data_2: (A(?data) & A(?data_2)) -> R_A_A(?data,?data_2)")
ltnw.axiom("forall ?data, ?data_2: R_A_A(?data,?data_2) -> (A(?data) & A(?data_2))")
def testPredicate(self):
p1=ltnw.predicate("P1",2)
p2=ltnw.predicate("P2",2)
self.assertEqual(ltnw.predicate("P1"),p1)
self.assertEqual(ltnw.predicate("P2"),p2)
self.assertNotEqual(ltnw.predicate("P1"),p2)