def convert(self, init):
"""Converts strings into exprs"""
try:
init = conjuncts(expr(init))
except AttributeError:
init = expr(init)
return init
def run_minisat_test():
"""
Test connection to MiniSat
"""
import logic
queries = [("(P | ~P)", True), # SAT
("(P & ~P)", False), # UNSAT
("(P | R) <=> (~(Q | R) & (R >> ~(S <=> T)))", True) # SAT
]
print "Running simple MiniSat test:"
t = 1
failed = []
for query, expected_result in queries:
print "-----------------------------------------------------"
print "Test {0}".format(t)
print " Query: '{0}'".format(query)
query = logic.conjuncts(logic.to_cnf(logic.expr(query)))
result = minisat(query, None, variable=None, value=True, verbose=False)
print " Query CNF: {0}".format(query)
print " Result: {0} (Expected: {1})".format(result.success, expected_result)
if result.success != expected_result:
print " FAILURE: unexpected result."
failed.append(t)
if result.success:
print " Variable Assignment: {0}".format(result.varmap)
t += 1
print "-----------------------------------------------------"
if not failed:
print "Successfully passed {0} tests.".format(len(queries))
else:
print "Passed {0} test(s).".format(len(queries) - len(failed))
print "The following tests failed: {0}".format(failure)
print "DONE."
def run_minisat_test():
"""
Test connection to MiniSat
"""
import logic
queries = [("(P | ~P)", True), # SAT
("(P & ~P)", False), # UNSAT
("(P | R) <=> (~(Q | R) & (R >> ~(S <=> T)))", True) # SAT
]
print "Running simple MiniSat test:"
t = 1
failed = []
for query, expected_result in queries:
print "-----------------------------------------------------"
print "Test {0}".format(t)
print " Query: '{0}'".format(query)
query = logic.conjuncts(logic.to_cnf(logic.expr(query)))
result = minisat(query, None, variable=None, value=True, verbose=False)
print " Query CNF: {0}".format(query)
print " Result: {0} (Expected: {1})".format(result.success, expected_result)
if result.success != expected_result:
print " FAILURE: unexpected result."
failed.append(t)
if result.success:
print " Variable Assignment: {0}".format(result.varmap)
t += 1
print "-----------------------------------------------------"
if not failed:
print "Successfully passed {0} tests.".format(len(queries))
else:
print "Passed {0} test(s).".format(len(queries) - len(failed))
print "The following tests failed: {0}".format(failure)
print "DONE."
def prop_fc(kb, alpha):
old_clauses_len = 0
while old_clauses_len != len(kb.clauses):
old_clauses_len = len(kb.clauses)
for clause in set(kb.clauses):
if clause.op in ("==>", "<=>"):
if all(
map(lambda c: c in kb.clauses,
conjuncts(clause.args[0]))):
kb.clauses.update(conjuncts(clause.args[1]))
if clause.op in ("<==", "<=>"):
if all(
map(lambda c: c in kb.clauses,
conjuncts(clause.args[1]))):
kb.clauses.update(conjuncts(clause.args[0]))
if alpha in kb.clauses:
return True
return False
def resolution(KB, alpha):
"""Apply the resolution algorithm to determine if alpha can be inferred from KB.
Args:
KB: an instance of logic.PropKB
alpha: an instance of logic.Expr
Return True if KB |- alpha
"""
# We do not want to waste effort resolving clauses of the KB against
# one another directly, we only want to resolve clauses that contain
# information derived from alpha. tainted_clauses will be the set
# we grow.
tainted_clauses = set(
normalize(clause) for clause in logic.conjuncts(logic.to_cnf(~alpha)))
KB_clauses = [normalize(clause) for clause in KB.clauses]
new = set()
while True:
# clausesWith is a map from literals to clauses containing that literal.
clausesWith = collections.defaultdict(list)
for clause in list(tainted_clauses) + KB_clauses:
for literal in clause:
clausesWith[literal].append(clause)
# For each tainted clause, add a pair of that clause and any
# tainted or KB clause that matches it (i.e. opposes on one literal).
pairs = []
for clause0 in tainted_clauses:
for literal in clause0:
for clause1 in clausesWith[negate(literal)]:
pairs.append((literal, clause0, clause1))
# Resolve all the pairs found above. If any result in None, the
# resolution is a bust (provides no new information).
# If any result in False (empty set), we have reached a contradiction
# and proven our goal.
for literal, clause0, clause1 in pairs:
result = resolve(clause0, clause1, literal)
if result is not None:
if result == set(): return True
else: new.add(frozenset(result))
# We now survey all the new clauses. In order to want to keep them,
# they must not be a superset of any already-known clause (since that
# would provide no new information).
added = False
for clause in new:
if not any(
old_clause.issubset(clause)
for old_clause in list(tainted_clauses) + KB_clauses):
tainted_clauses.add(clause)
added = True
# If we have not found any new information, we've reached the end
# and cannot prove our goal (it may be True, it may be False, but we
# can't definitively say either way).
if not added: return False
def resolution(KB, alpha):
"""Apply the resolution algorithm to determine if alpha can be inferred from KB.
Args:
KB: an instance of logic.PropKB
alpha: an instance of logic.Expr
Return True if KB |- alpha
"""
# We do not want to waste effort resolving clauses of the KB against
# one another directly, we only want to resolve clauses that contain
# information derived from alpha. tainted_clauses will be the set
# we grow.
tainted_clauses = set(normalize(clause)
for clause in logic.conjuncts(logic.to_cnf(~alpha)))
KB_clauses = [normalize(clause) for clause in KB.clauses]
new = set()
while True:
# clausesWith is a map from literals to clauses containing that literal.
clausesWith = collections.defaultdict(list)
for clause in list(tainted_clauses) + KB_clauses:
for literal in clause:
clausesWith[literal].append(clause)
# For each tainted clause, add a pair of that clause and any
# tainted or KB clause that matches it (i.e. opposes on one literal).
pairs = []
for clause0 in tainted_clauses:
for literal in clause0:
for clause1 in clausesWith[negate(literal)]:
pairs.append((literal, clause0, clause1))
# Resolve all the pairs found above. If any result in None, the
# resolution is a bust (provides no new information).
# If any result in False (empty set), we have reached a contradiction
# and proven our goal.
for literal, clause0, clause1 in pairs:
result = resolve(clause0, clause1, literal)
if result is not None:
if result == set(): return True
else: new.add(frozenset(result))
# We now survey all the new clauses. In order to want to keep them,
# they must not be a superset of any already-known clause (since that
# would provide no new information).
added = False
for clause in new:
if not any(old_clause.issubset(clause)
for old_clause in list(tainted_clauses) + KB_clauses):
tainted_clauses.add(clause)
added = True
# If we have not found any new information, we've reached the end
# and cannot prove our goal (it may be True, it may be False, but we
# can't definitively say either way).
if not added: return False
def convert(self, clauses):
"""Converts strings into Exprs"""
if isinstance(clauses, Expr):
clauses = conjuncts(clauses)
for i in range(len(clauses)):
if clauses[i].op == '~':
clauses[i] = expr('Not' + str(clauses[i].args[0]))
elif isinstance(clauses, str):
clauses = clauses.replace('~', 'Not')
if len(clauses) > 0:
clauses = expr(clauses)
try:
clauses = conjuncts(clauses)
except AttributeError:
pass
return clauses
def convert(self, clauses):
"""Converts strings into Exprs"""
if isinstance(clauses, Expr):
clauses = conjuncts(clauses)
for i in range(len(clauses)):
if clauses[i].op == '~':
clauses[i] = expr('Not' + str(clauses[i].args[0]))
elif isinstance(clauses, str):
clauses = clauses.replace('~', 'Not')
if len(clauses) > 0:
clauses = expr(clauses)
try:
clauses = conjuncts(clauses)
except AttributeError:
pass
return clauses
def convert(self, precond, effect):
"""Converts strings into Exprs"""
precond = precond.replace('~', 'Not')
if len(precond) > 0:
precond = expr(precond)
effect = effect.replace('~', 'Not')
if len(effect) > 0:
effect = expr(effect)
try:
precond = conjuncts(precond)
except AttributeError:
pass
try:
effect = conjuncts(effect)
except AttributeError:
pass
return precond, effect
def ask(self, prop):
to_prove = frozenset(map(frozenset,
map(set,
map(disjuncts,
conjuncts(to_cnf(~prop)))))) \
| self.clauses #把要证明的结论先否定再整理成CNF的形式，再和原来KB中的子句们并一下
if fast_dpll(to_prove):
return False #是否有contradiction,若没有（fast_dpll()为True）
else:
self.tell(prop) #如果结论成立(有contradiction)，那么就把新的推论给到KB
return True
def ask(self, prop):
to_prove = frozenset(map(frozenset,
map(set,
map(disjuncts,
conjuncts(to_cnf(~prop)))))) \
| self.clauses
if fast_dpll(to_prove):
return False
else:
self.tell(prop)
return True
def convert(self, clauses):
"""Converts strings into exprs"""
if not isinstance(clauses, Expr):
if len(clauses) > 0:
clauses = expr(clauses)
else:
clauses = []
try:
clauses = conjuncts(clauses)
except AttributeError:
clauses = clauses
return clauses
def test_action():
precond = 'At(c, a) & At(p, a) & Cargo(c) & Plane(p) & Airport(a)'
effect = 'In(c, p) & ~At(c, a)'
a = Action('Load(c, p, a)', precond, effect)
args = [expr("C1"), expr("P1"), expr("SFO")]
assert a.substitute(expr("Load(c, p, a)"), args) == expr("Load(C1, P1, SFO)")
test_kb = FolKB(conjuncts(expr('At(C1, SFO) & At(C2, JFK) & At(P1, SFO) & At(P2, JFK) & Cargo(C1) & Cargo(C2) & Plane(P1) & Plane(P2) & Airport(SFO) & Airport(JFK)')))
assert a.check_precond(test_kb, args)
a.act(test_kb, args)
assert test_kb.ask(expr("In(C1, P2)")) is False
assert test_kb.ask(expr("In(C1, P1)")) is not False
assert test_kb.ask(expr("Plane(P2)")) is not False
assert not a.check_precond(test_kb, args)
def convert(self, clauses):
"""Converts strings into exprs"""
if not isinstance(clauses, Expr):
if len(clauses) > 0:
clauses = expr(clauses)
else:
clauses = []
try:
clauses = conjuncts(clauses)
except AttributeError:
clauses = clauses
new_clauses = []
for clause in clauses:
if clause.op == '~':
new_clauses.append(expr('Not' + str(clause.args[0])))
else:
new_clauses.append(clause)
return new_clauses
def is_valid_cnf(exp):
if not isinstance(exp, Expr):
print "Input is not an expression."
return False
clauses = conjuncts(exp);
for c in clauses:
literals = disjuncts(c)
for lit in literals:
if len(lit.args) == 0:
symbol = lit;
elif len(lit.args) == 1:
symbol = lit.args[0]
if len(symbol.args) != 0:
print "Found a NOT outside of %s" % symbol
return False
else:
print "Found %s where only a literal should be." % lit
return False
symbol_str = str(symbol)
if not is_symbol(symbol_str):
print "%s is not a valid symbol." % symbol_str
return False
elif not symbol_str[0].isupper():
print "The symbol %s must begin with an upper-case letter." % symbol_str
return False
elif symbol_str == 'TRUE':
print "TRUE is not a valid symbol." % symbol_str
return False
elif symbol_str == 'FALSE':
print "FALSE is not a valid symbol." % symbol_str
return False
return True
def is_valid_cnf(exp):
if not isinstance(exp, Expr):
print "Input is not an expression."
return False
clauses = conjuncts(exp)
for c in clauses:
literals = disjuncts(c)
for lit in literals:
if len(lit.args) == 0:
symbol = lit
elif len(lit.args) == 1:
symbol = lit.args[0]
if len(symbol.args) != 0:
print "Found a NOT outside of %s" % symbol
return False
else:
print "Found %s where only a literal should be." % lit
return False
symbol_str = str(symbol)
if not is_symbol(symbol_str):
print "%s is not a valid symbol." % symbol_str
return False
elif not symbol_str[0].isupper():
print "The symbol %s must begin with an upper-case letter." % symbol_str
return False
elif symbol_str == 'TRUE':
print "TRUE is not a valid symbol." % symbol_str
return False
elif symbol_str == 'FALSE':
print "FALSE is not a valid symbol." % symbol_str
return False
return True
def result(self, state, action):
terms = parse_state(state)
sentence = str(
logic.associate(
'&',
action(logic.conjuncts(state), action.args).clauses))
#print('------------\nBefore: ' + sentence)
while sentence.find('divide(x)') != -1:
quotient = terms[4] / terms[0]
terms[0] = 1
terms[4] = quotient
sentence = sentence.replace('divide(x)', '{:.2f}'.format(quotient))
while sentence.find('combine') != -1:
start = sentence.find('combine')
term = int(sentence[start + 9]) - 1
if term < 3:
new_val = terms[term] + terms[2]
terms[term] = new_val
terms[2] = 0
else:
new_val = terms[term] + terms[5]
terms[term] = new_val
terms[5] = 0
sentence = sentence.replace(sentence[start:(start + 11)],
str(new_val))
while sentence.find('inverse') != -1:
start = sentence.find('inverse')
term = int(sentence[start + 9]) - 1
new_val = -1 * terms[term]
if term == 3:
terms[2] = new_val
elif term == 1:
terms[5] = new_val
terms[term] = 0
sentence = sentence.replace(sentence[start:(start + 11)],
str(new_val))
#print('After: ' + sentence + '\n------------')
return logic.associate('&', self.convert(sentence.replace('Not', '~')))
def tell(self, sentence):
self.clauses.update(
map(frozenset, map(set, map(disjuncts,
conjuncts(to_cnf(sentence))))))
def goal_test(self):
"""Checks if the goals have been reached"""
return all(goal in self.init for goal in conjuncts(self.goals))