def is_equal_to(a1, a2):
# verificăm atomi cu același nume de predicat și același număr de argumente
if not (is_atom(a1) and is_atom(a2) and get_head(a1) == get_head(a2)
and len(get_args(a1)) == len(get_args(a2))):
return False
return all([
equal_terms(get_args(a1)[i],
get_args(a2)[i]) for i in range(len(get_args(a1)))
])
def equal_terms(t1, t2):
if is_constant(t1) and is_constant(t2):
return get_value(t1) == get_value(t2)
if is_variable(t1) and is_variable(t2):
return get_name(t1) == get_name(t2)
if is_function_call(t1) and is_function(t2):
if get_head(t1) != get_head(t2):
return all([equal_terms(get_args(t1)[i], get_args(t2)[i]) for i in range(len(get_args(t1)))])
return False
def get_conclusion(formula):
# TODO
ans = None
for i in get_args(formula):
if is_atom(i):
ans = i
return ans
def get_premises(formula):
# TODO
ans = []
for i in get_args(formula):
if is_negative_literal(i):
ans.append(i)
return ans
def checkMathPredicates(name, atom, subst = None): args = get_args(atom) if is_variable(args[0]) or is_variable(args[1]): return False a = get_value(args[0]) b = get_value(args[1]) if name == 'isBigger': return a >= b elif name == 'isSmaller': return a < b elif name == 'equal': return a == b elif name == 'sum': if is_constant(args[2]) and (a + b == get_value(args[2])): return True elif is_variable(args[2]): subst[get_name(args[2])] = make_const(a + b) return True elif name == 'dif': if is_constant(args[2]) and (a - b == get_value(args[2])): return True elif is_variable(args[2]): subst[get_name(args[2])] = make_const(a - b) return True return False
def checkMathPredicates(name, atom):
args = get_args(atom)
if is_variable(args[0]) or is_variable(args[1]):
return False
a = get_value(args[0])
b = get_value(args[1])
if name == 'isBigger':
return a >= b
elif name == 'equal':
return a == b
elif name == 'sum':
if is_constant(args[2]) and (a + b == get_value(args[2])):
return True
elif is_variable(args[2]):
args[2] = substitute(args[2],
{get_name(args[2]): make_const(a + b)})
return True
elif name == 'dif':
if is_constant(args[2]) and (a - b == get_value(args[2])):
return True
elif is_variable(args[2]):
args[2] = substitute(args[2],
{get_name(args[2]): make_const(a - b)})
return True
return False
def forward_chaining(kb, theorem, verbose=True):
# Salvăm baza de date originală, lucrăm cu o copie
local_kb = deepcopy(kb)
# Două variabile care descriu starea căutării
got_new_facts = True # s-au găsit fapte noi la ultima căutare
is_proved = False # a fost demostrată teorema
# Verificăm dacă teorema este deja demonstrată
for fact in filter(is_fact, local_kb):
if unify(fact, theorem):
if verbose:
print("This already in KB: " + print_formula(fact, True))
is_proved = True
break
while (not is_proved) and got_new_facts:
got_new_facts = False
for rule in filter(is_rule, local_kb):
# Pentru fiecare regulă
new_facts = apply_rule(rule, list(filter(is_fact, local_kb)))
new_facts = list(
filter(
lambda fact: not any(
list(
filter(lambda orig: is_equal_to(fact, orig),
local_kb))), new_facts))
if new_facts:
if verbose:
print("Applied rule: " + print_formula(rule, True) +
", obtained " + str(len(new_facts)) + " new facts.")
if any(filter(lambda t: is_variable(t), get_args(get_conclusion(rule)))) and \
any(filter(lambda fact: is_equal_to(fact, get_conclusion(rule)), new_facts)):
print(
"Demonstration is too general, the conclusion is not instantiated (facts obtained:",
",".join([print_formula(f, True)
for f in new_facts]), ").")
return False
got_new_facts = True
for fact in new_facts:
#if verbose: print("New fact: " + print_formula(fact, True))
if unify(fact, theorem) != False:
is_proved = True
add_statement(local_kb, fact)
if verbose:
print("Now in KB: " + print_formula(fact, True))
break
add_statement(local_kb, fact)
if is_proved:
break
if verbose:
if is_proved:
print("The theorem is TRUE!")
else:
print("The theorem is FALSE!")
return is_proved
def apply_rule(rule, facts):
print(facts)
resulting_facts = []
premises = list(map(lambda x: get_args(x)[0], get_premises(rule)))
print premises
substitutions = []
for premise in premises:
print('*** premise ***')
print(premise)
print('*** end premise ***')
new_substitutions = []
for fact in facts:
print('*** premise ***')
print(fact)
print('*** end premise ***')
res = unify(premise, fact)
if res:
substitutions.append(res)
for substitution in substitutions:
res = unify(premise, fact, substitution)
if res:
new_substitutions.append(res)
for new_subst in new_substitutions:
substitutions.append(new_subst)
print(substitutions)
for subst in substitutions:
res = substitute(get_conclusion(rule), subst)
if res and res not in resulting_facts:
resulting_facts.append(res)
return resulting_facts
def apply_rule(rule, facts):
# TODO
subst = {}
prem = {}
ans = []
values = {}
fact_values = {}
for fact in facts:
vals = []
for arg in get_args(fact):
vals.append(get_value(arg))
if get_head(fact) not in values:
values[get_head(fact)] = [tuple(vals)]
else:
values[get_head(fact)].append(tuple(vals))
if get_head(fact) not in fact_values:
fact_values[get_head(fact)] = [fact]
else:
fact_values[get_head(fact)].append(fact)
for r in get_premises(rule):
if isinstance(r, Sentence):
var = get_name(get_args(get_args(r)[0])[0])
prm = get_head(get_args(r)[0])
prem[(prm, var)] = get_args(r)[0]
continue
var = get_name(get_args(r)[0])
prem[(get_head(r), var)] = [r]
index_h = {}
max_index_h = {}
for (pred, var) in prem:
index_h[(pred, var)] = 0
max_index_h[(pred, var)] = 0
if pred in values:
max_index_h[(pred, var)] = len(values[pred])
pred = []
for x in prem:
pred.append(x)
current_p = 0
subst = {}
while 1:
p = pred[current_p]
prd = p[0]
val = p[1]
p_index = index_h[p]
if p_index == max_index_h[p]:
index_h[p] = 0
if current_p == 0:
break
current_p = current_p - 1
p = pred[current_p]
for x in get_args(prem[p]):
name = get_name(x)
if name in subst:
del subst[name]
index_h[p] = index_h[p] + 1
continue
b_subst = deepcopy(subst)
aux_subst = unify(prem[p], fact_values[prd][p_index], subst)
if aux_subst!=False:
subst = aux_subst
if current_p == len(pred) - 1:
ans.append(substitute(get_conclusion(rule),subst))
subst = {}
current_p = 0
next_index = index_h[p] + 1
index_h[p] = next_index
p = pred[current_p]
continue
else:
subst = b_subst
index_h[p] = index_h[p] + 1
if index_h[p] == max_index_h[p]:
index_h[p] = 0
current_p = current_p - 1
index_h[pred[current_p]] = index_h[pred[current_p]] + 1
p = pred[current_p]
for x in get_args(prem[p]):
name = get_name(x)
if name in subst:
del subst[name]
continue
if current_p < len(pred) - 1:
current_p = current_p + 1
continue
index_h[p] = index_h[p] + 1
return ans
def is_rule(formula):
# TODO
for i in get_args(formula):
if is_negative_literal(i):
return True
return False
def get_conclusion(formula):
for arg in get_args(formula):
if is_positive_literal(arg):
return arg
def get_premises(formula):
premises = []
for arg in get_args(formula):
if is_negative_literal(arg):
premises.append(arg)
return premises
