def setUp(self):
"""Set up test fixtures, if any."""
self.a_sym = Symbol("a")
self.b_sym = Symbol("b")
self.c_sym = Symbol("c")
self.alphabet = Alphabet({self.a_sym, self.b_sym, self.c_sym})
# Propositions
self.a = AtomicFormula(self.a_sym)
self.b = AtomicFormula(self.b_sym)
self.c = AtomicFormula(self.c_sym)
self.not_a = Not(self.a)
self.not_a_and_b = And(self.not_a, self.b)
self.not_a_or_c = Or(self.not_a, self.c)
self.true = TrueFormula()
self.false = FalseFormula()
self.symbol2truth = {
self.a_sym: True,
self.b_sym: False,
self.c_sym: True
}
self.I = PLInterpretation(self.alphabet, self.symbol2truth)
self.PL = PL(self.alphabet)
def test_to_nnf_allowed_formulas_not_normalized(self):
a_sym = Symbol("a")
b_sym = Symbol("b")
alphabet = Alphabet({a_sym, b_sym})
a = AtomicFormula(a_sym)
b = AtomicFormula(b_sym)
pl = PL(alphabet)
self.assertEqual(pl.to_nnf(Not(Not(b))), b)
self.assertEqual(pl.to_nnf(Not(And(a, Not(b)))), Or(Not(a), b))
def test_to_nnf_derived_formula(self):
a_sym = Symbol("a")
b_sym = Symbol("b")
alphabet = Alphabet({a_sym, b_sym})
a = AtomicFormula(a_sym)
b = AtomicFormula(b_sym)
pl = PL(alphabet)
self.assertEqual(pl.to_nnf(Not(Or(b, Not(a)))), And(Not(b), a))
self.assertEqual(pl.to_nnf(Not(Implies(b, Not(a)))), And(b, a))
def test_expand_formula_allowed_formulas(self):
a_sym = Symbol("a")
b_sym = Symbol("b")
alphabet = Alphabet({a_sym, b_sym})
a = AtomicFormula(a_sym)
b = AtomicFormula(b_sym)
pl = PL(alphabet)
self.assertEqual(pl.expand_formula(a), a)
self.assertEqual(pl.expand_formula(Not(b)), Not(b))
self.assertEqual(pl.expand_formula(And(a, b)), And(a, b))
def test_find_atomics(self):
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
atomic_a = AtomicFormula(a)
atomic_b = AtomicFormula(b)
atomic_c = AtomicFormula(c)
self.assertEqual(
PL.find_atomics(And(atomic_a, And(atomic_b, atomic_c))),
{atomic_a, atomic_b, atomic_c})
self.assertEqual(PL.find_atomics(Or(atomic_a, Or(atomic_b, atomic_c))),
{atomic_a, atomic_b, atomic_c})
self.assertEqual(
PL.find_atomics(Equivalence(atomic_a, Or(atomic_b, atomic_c))),
{atomic_a, atomic_b, atomic_c})
def test_powerset(self):
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
d = Symbol("d")
s = [a,b,c,d]
true_ps = {
(),
(a,),(b,),(c,),(d,),
(a, b), (a, c), (a, d), (b, c), (b, d), (c, d),
(a,b,c), (a,b,d), (a,c,d), (b,c,d),
(a, b, c, d)
}
set_true_ps_frozenset = {frozenset(t) for t in true_ps}
self.assertEqual(set(powerset(s)), set_true_ps_frozenset)
def test_expand_formula_error(self):
a_sym = Symbol("a")
alphabet = Alphabet({a_sym})
a = Next(AtomicFormula(a_sym))
pl = PL(alphabet)
with self.assertRaises(ValueError) as ve:
pl.expand_formula(a)
def __init__(self, env):
super().__init__(env)
self.row_symbols = [Symbol(r) for r in ["r0", "r1", "r2"]]
self.dfa = self._build_automata()
self.goal_reward = 1000
self.transition_reward = 100
self.simulator = Simulator(self.dfa)
self.last_status = None
def test_is_formula_composed(self):
a_sym = Symbol("a")
alphabet = Alphabet({a_sym})
a = AtomicFormula(a_sym)
pl = PL(alphabet)
self.assertTrue(
pl.is_formula(
Implies(Not(a), And(TrueFormula(), Not(FalseFormula())))))
self.assertFalse(
pl.is_formula(
Implies(Not(a), And(TrueFormula(), Next(FalseFormula())))))
def setUp(self):
# Symbols
self.a_sym = Symbol("a")
self.b_sym = Symbol("b")
self.c_sym = Symbol("c")
# Propositions
self.a = AtomicFormula(self.a_sym)
self.b = AtomicFormula(self.b_sym)
self.c = AtomicFormula(self.c_sym)
self.alphabet = Alphabet({self.a_sym, self.b_sym, self.c_sym})
self.ref = REf(self.alphabet)
self.trace_1_list = [
{self.a_sym, self.b_sym},
{self.a_sym, self.c_sym},
{self.a_sym, self.b_sym},
{self.a_sym, self.c_sym},
{self.b_sym, self.c_sym},
]
self.trace_1 = FiniteTrace(self.trace_1_list, self.alphabet)
def test_expand_formula_derived_formulas(self):
a_sym = Symbol("a")
b_sym = Symbol("b")
alphabet = Alphabet({a_sym, b_sym})
a = AtomicFormula(a_sym)
b = AtomicFormula(b_sym)
# T = Not(And(Not(DUMMY_ATOMIC), DUMMY_ATOMIC))
# F = And(Not(DUMMY_ATOMIC), DUMMY_ATOMIC)
T = TrueFormula()
F = FalseFormula()
pl = PL(alphabet)
self.assertEqual(pl.expand_formula(TrueFormula()), T)
self.assertEqual(pl.expand_formula(FalseFormula()), F)
self.assertEqual(pl.expand_formula(Or(a, b)), Not(And(Not(a), Not(b))))
self.assertEqual(pl.expand_formula(Implies(a, b)),
Not(And(Not(Not(a)), Not(b))))
self.assertEqual(pl.expand_formula(Implies(b, a)),
Not(And(Not(Not(b)), Not(a))))
# A === B = (A AND B) OR (NOT A AND NOT B) = NOT( NOT(A AND B) AND NOT(NOT A AND NOT B) )
self.assertEqual(pl.expand_formula(Equivalence(a, b)),
Not(And(Not(And(a, b)), Not(And(Not(a), Not(b))))))
def test_expand_formula_composed(self):
a_sym = Symbol("a")
alphabet = Alphabet({a_sym})
a = AtomicFormula(a_sym)
# T = Not(And(Not(DUMMY_ATOMIC), DUMMY_ATOMIC))
# F = And(Not(DUMMY_ATOMIC), DUMMY_ATOMIC)
T = TrueFormula()
F = FalseFormula()
pl = PL(alphabet)
self.assertEqual(pl.expand_formula(And(TrueFormula(), FalseFormula())),
And(T, F))
self.assertEqual(pl.expand_formula(Or(TrueFormula(), FalseFormula())),
Not(And(Not(T), Not(F))))
self.assertEqual(
pl.expand_formula(Implies(TrueFormula(), FalseFormula())),
Not(And(Not(Not(T)), Not(F))))
self.assertEqual(
pl.expand_formula(Equivalence(TrueFormula(), FalseFormula())),
Not(And(Not(And(T, F)), Not(And(Not(T), Not(F))))))
def fromString(cls, name:str):
return Variable(Symbol(name))
def test_chain(self):
a_sym, b_sym, c_sym = [Symbol(s) for s in ["a", "b", "c"]]
a, b, c = [AtomicFormula(s) for s in [a_sym,b_sym,c_sym]]
and_chain = And.chain([a, b, c])
self.assertEqual(and_chain, And(a, And(b, And(c, TrueFormula()))))
def test_is_formula_error(self):
a_sym = Symbol("a")
alphabet = Alphabet({a_sym})
a = Next(AtomicFormula(a_sym))
pl = PL(alphabet)
self.assertFalse(pl.is_formula(a))
def fromStrings(symbol_strings:Set[str]):
return Alphabet(set(Symbol(s) for s in symbol_strings))
def test_is_formula_atomic(self):
a_sym = Symbol("a")
alphabet = Alphabet({a_sym})
a = AtomicFormula(a_sym)
pl = PL(alphabet)
self.assertTrue(pl.is_formula(a))
def test_minimal_models(self):
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
alphabet = Alphabet({a, b, c})
pl = PL(alphabet)
atomic_a = AtomicFormula(a)
atomic_b = AtomicFormula(b)
atomic_c = AtomicFormula(c)
self.assertEqual(
pl.minimal_models(TrueFormula()),
{PLInterpretation(alphabet, {
a: False,
b: False,
c: False
})})
self.assertEqual(pl.minimal_models(FalseFormula()), set())
self.assertEqual(
pl.minimal_models(atomic_a),
{PLInterpretation(alphabet, {
a: True,
b: False,
c: False
})})
self.assertEqual(
pl.minimal_models(Not(atomic_a)),
{PLInterpretation(alphabet, {
a: False,
b: False,
c: False
})})
self.assertEqual(
pl.minimal_models(And(atomic_a, atomic_b)),
{PLInterpretation(alphabet, {
a: True,
b: True,
c: False
})})
self.assertEqual(pl.minimal_models(And(atomic_a, Not(atomic_a))),
set())
self.assertEqual(
pl.minimal_models(Or(atomic_a, atomic_b)), {
PLInterpretation(alphabet, {
a: False,
b: True,
c: False
}),
PLInterpretation(alphabet, {
a: True,
b: False,
c: False
})
})
self.assertEqual(
pl.minimal_models(And.chain([atomic_a, atomic_b, atomic_c])),
{PLInterpretation(alphabet, {
a: True,
b: True,
c: True
})})
def setUp(self):
"""Set up test fixtures, if any."""
# Symbols
self.a_sym = Symbol("a")
self.b_sym = Symbol("b")
self.c_sym = Symbol("c")
# Propositions
self.a = AtomicFormula(self.a_sym)
self.b = AtomicFormula(self.b_sym)
self.c = AtomicFormula(self.c_sym)
# Propositionals
self.not_a = Not(self.a)
self.not_b = Not(self.b)
self.not_c = Not(self.c)
self.a_and_b = And(self.a, self.b)
self.a_and_c = And(self.a, self.c)
self.b_and_c = And(self.b, self.c)
self.abc = And(self.a, And(self.b, self.c))
self.b_or_c = Or(self.b, self.c)
self.a_or_b = Or(self.a, self.b)
self.not_abc = Not(And(self.a, And(self.b, self.c)))
### Path expression
# Tests
self.test_a = PathExpressionTest(self.a)
self.test_b = PathExpressionTest(self.b)
self.test_not_a = PathExpressionTest(self.not_a)
self.test_not_b = PathExpressionTest(self.not_b)
# Union
self.path_a_or_b = PathExpressionUnion(self.a, self.b)
self.path_b_or_c = PathExpressionUnion(self.b, self.c)
# Sequence
self.path_seq_a_and_b__a_and_c = PathExpressionSequence(
self.a_and_b, self.a_and_c)
self.path_a_or_b__b_or_c = PathExpressionSequence(
self.path_a_or_b, self.path_b_or_c)
# Stars
self.path_b_or_c_star = PathExpressionStar(self.path_b_or_c)
self.path_not_abc = PathExpressionStar(self.not_abc)
# Modal connective
self.eventually_propositional_a_and_b__a_and_c = PathExpressionEventually(
self.a_and_b, self.a_and_c)
self.eventually_test_a__c = PathExpressionEventually(
self.test_a, self.c)
self.eventually_test_a__b = PathExpressionEventually(
self.test_a, self.b)
self.eventually_seq_a_and_b__a_and_c__not_c = PathExpressionEventually(
self.path_seq_a_and_b__a_and_c, self.not_c)
self.eventually_seq_a_and_b__a_and_c__c = PathExpressionEventually(
self.path_seq_a_and_b__a_and_c, self.c)
self.eventually_b_or_c_star__b_and_c = PathExpressionEventually(
self.path_b_or_c_star, self.b_and_c)
self.next_a_and_c = PathExpressionEventually(TrueFormula(),
self.a_and_c)
self.liveness_b_and_c = PathExpressionEventually(
PathExpressionStar(TrueFormula()), self.b_and_c)
self.liveness_abc = PathExpressionEventually(
PathExpressionStar(TrueFormula()), self.abc)
self.always_true__a = PathExpressionAlways(
PathExpressionStar(TrueFormula()), self.a)
self.always_true__b_or_c = PathExpressionAlways(
PathExpressionStar(TrueFormula()), self.b_or_c)
self.alphabet = Alphabet({self.a_sym, self.b_sym, self.c_sym})
# Traces
self.ldlf = LDLf(self.alphabet)
self.trace_1_list = [
{self.a_sym, self.b_sym},
{self.a_sym, self.c_sym},
{self.a_sym, self.b_sym},
{self.a_sym, self.c_sym},
{self.b_sym, self.c_sym},
]
self.trace_1 = FiniteTrace(self.trace_1_list, self.alphabet)
def _members(self):
return (Symbol(Symbols.LOGICAL_FALSE.value))
def __str__(self):
return str(Symbol(Symbols.LOGICAL_FALSE.value))
def _members(self):
return (Symbol(Symbols.END.value))
def __str__(self):
return str(Symbol(Symbols.END.value))
def to_nfa(self, f: Formula):
# TODO: optimize!!!
assert self.is_formula(f)
nnf_f = self.to_nnf(f)
alphabet = powerset(self.alphabet.symbols)
initial_states = {frozenset([nnf_f])}
final_states = {frozenset()}
delta = set()
pl, I = PL._from_set_of_propositionals(set(), Alphabet(set()))
d = self.delta(nnf_f, frozenset(), epsilon=True)
if pl.truth(d, I):
final_states.add(frozenset([nnf_f]))
states = {frozenset(), frozenset([nnf_f])}
states_changed, delta_changed = True, True
while states_changed or delta_changed:
states_changed, delta_changed = False, False
for actions_set in alphabet:
states_list = list(states)
for q in states_list:
delta_formulas = [
self.delta(subf, actions_set) for subf in q
]
atomics = [
s for subf in delta_formulas
for s in PL.find_atomics(subf)
]
symbol2formula = {
Symbol(str(f)): f
for f in atomics
if f != TrueFormula() and f != FalseFormula()
}
formula2atomic_formulas = {
f: AtomicFormula.fromName(str(f))
if f != TrueFormula() and f != FalseFormula() else f
for f in atomics
}
transformed_delta_formulas = [
self._tranform_delta(f, formula2atomic_formulas)
for f in delta_formulas
]
conjunctions = And.chain(transformed_delta_formulas)
models = frozenset(
PL(Alphabet(
set(symbol2formula))).minimal_models(conjunctions))
if len(models) == 0:
continue
for min_model in models:
q_prime = frozenset({
symbol2formula[s]
for s in min_model.symbol2truth
if min_model.symbol2truth[s]
})
len_before = len(states)
states.add(q_prime)
if len(states) == len_before + 1:
states_list.append(q_prime)
states_changed = True
len_before = len(delta)
delta.add((q, actions_set, q_prime))
if len(delta) == len_before + 1:
delta_changed = True
# check if q_prime should be added as final state
if len(q_prime) == 0:
final_states.add(q_prime)
else:
q_prime_delta_conjunction = And.chain([
self.delta(subf, frozenset(), epsilon=True)
for subf in q_prime
])
pl, I = PL._from_set_of_propositionals(
set(), Alphabet(set()))
if pl.truth(q_prime_delta_conjunction, I):
final_states.add(q_prime)
return {
"alphabet": alphabet,
"states": frozenset(states),
"initial_states": frozenset(initial_states),
"transitions": delta,
"accepting_states": frozenset(final_states)
}
def fromName(cls, name: str):
return cls(Symbol(name))
def setUp(self):
"""Set up symbols, terms and formulas. Both legal and illegal, according to some FOL system"""
# Symbols
self.a_sym = Symbol('a')
self.b_sym = Symbol('b')
self.const_sym = ConstantSymbol("Const")
self.fun_sym = FunctionSymbol("Fun", 3)
self.predicate_sym = PredicateSymbol("Predicate", 2)
self.A = PredicateSymbol("A", 1)
# Terms
self.a = Variable(self.a_sym)
self.b = Variable(self.b_sym)
self.c = Variable.fromString("c")
self.const = ConstantTerm(self.const_sym)
self.fun_abc = FunctionTerm(self.fun_sym, self.a, self.b, self.c)
# Formulas
self.predicate_ab = PredicateFormula(self.predicate_sym, self.a,
self.b)
self.predicate_ac = PredicateFormula(self.predicate_sym, self.a,
self.c)
self.A_a = PredicateFormula(self.A, self.a)
self.a_equal_a = Equal(self.a, self.a)
self.b_equal_c = Equal(self.b, self.c)
self.neg_a_equal_a = Not(self.a_equal_a)
self.neg_Aa = Not(self.A_a)
self.Aa_and_b_equal_c = And(self.A_a, self.b_equal_c)
self.Aa_or_b_equal_c = Or(self.A_a, self.b_equal_c)
self.Aa_implies_b_equal_c = Implies(self.A_a, self.b_equal_c)
self.exists_a_predicate_ab = Exists(self.a, self.predicate_ab)
self.forall_b_exists_a_predicate_ab = ForAll(
self.b, self.exists_a_predicate_ab)
# FOL
self.vars = {self.a, self.b, self.c}
self.functions = {self.const_sym, self.fun_sym}
self.predicates = {self.predicate_sym, self.A}
self.alphabet = FOLAlphabet(self.functions, self.predicates)
self.myFOL = FOL(self.alphabet)
# define dummy stuff
# does not belong to myFOL. They are used for test membership to myFOL
self.dummy_variable = Variable.fromString(
"ThisVariableDoesNotBelongToFOLSystem")
self.dummy_fun_sym = FunctionSymbol(
"ThisFunctionDoesNotBelongToFOLSystem", 3)
self.dummy_constant_sym = ConstantSymbol(
"ThisConstDoesNotBelongToFOLSystem")
self.dummy_predicate_sym = PredicateSymbol(
"ThisPredicateDoesNotBelongToFOLSystem", 2)
self.dummy_fun = FunctionTerm(self.dummy_fun_sym, self.a, self.b,
self.dummy_variable)
self.dummy_constant = ConstantTerm(self.dummy_constant_sym)
self.dummy_predicate = PredicateFormula(self.dummy_predicate_sym,
self.a, self.b)
self.dummy_predicate_only_one_symbol_false = PredicateFormula(
self.predicate_sym, self.dummy_variable, self.dummy_constant)
self.dummy_equal = Equal(self.c, self.dummy_constant)
self.dummy_neg = Not(self.dummy_predicate_only_one_symbol_false)
self.dummy_and = And(self.dummy_predicate, self.predicate_ab)
self.dummy_or = Or(self.dummy_predicate_only_one_symbol_false,
self.predicate_ac)
self.dummy_exists = Exists(self.dummy_variable,
self.dummy_predicate_only_one_symbol_false)
self.dummy_forall = ForAll(self.b, self.dummy_predicate)
def test_eq(self):
# Symbols
self.assertEqual(self.a_sym, self.a_sym)
self.assertEqual(self.a_sym, Symbol("a"))
self.assertEqual(self.const_sym, ConstantSymbol("Const"))
self.assertEqual(self.fun_sym, FunctionSymbol("Fun", 3))
self.assertEqual(self.predicate_sym, PredicateSymbol("Predicate", 2))
self.assertNotEqual(self.a_sym, Symbol("c"))
self.assertNotEqual(self.const_sym, ConstantSymbol("Another_Const"))
self.assertNotEqual(self.fun_sym, FunctionSymbol("Another_Fun", 3))
self.assertNotEqual(self.fun_sym, FunctionSymbol("Fun", 2))
self.assertNotEqual(self.predicate_sym,
PredicateSymbol("Another_Predicate", 2))
self.assertNotEqual(self.predicate_sym,
PredicateSymbol("Predicate", 1))
self.assertNotEqual(self.a_sym, self.fun_sym)
self.assertNotEqual(self.const_sym, self.fun_sym)
# Terms
self.assertEqual(self.a, self.a)
self.assertEqual(self.a, Variable.fromString("a"))
self.assertEqual(self.const, ConstantTerm(ConstantSymbol("Const")))
self.assertEqual(
self.fun_abc,
FunctionTerm(FunctionSymbol("Fun", 3), self.a, self.b, self.c))
self.assertNotEqual(self.a, self.b)
self.assertNotEqual(self.a, Variable.fromString("c"))
self.assertNotEqual(self.const,
ConstantTerm(ConstantSymbol("Another_Const")))
self.assertNotEqual(
self.fun_abc,
FunctionTerm(FunctionSymbol("Another_Fun", 3), self.a, self.b,
self.c))
self.assertNotEqual(
self.fun_abc,
FunctionTerm(FunctionSymbol("Fun", 3), self.a, self.b, self.a))
self.assertNotEqual(self.a, self.fun_abc)
# Formulas
self.assertEqual(
self.predicate_ab,
PredicateFormula(PredicateSymbol("Predicate", 2),
Variable.fromString("a"),
Variable.fromString("b")))
self.assertEqual(
self.A_a,
PredicateFormula(PredicateSymbol("A", 1),
Variable.fromString("a")))
self.assertEqual(
self.b_equal_c,
Equal(Variable.fromString("b"), Variable.fromString("c")))
self.assertEqual(
self.neg_a_equal_a,
Not(Equal(Variable.fromString("a"), Variable.fromString("a"))))
self.assertEqual(
self.forall_b_exists_a_predicate_ab,
ForAll(
Variable.fromString("b"),
Exists(
Variable.fromString("a"),
PredicateFormula(PredicateSymbol("Predicate", 2),
Variable.fromString("a"),
Variable.fromString("b")))))
self.assertNotEqual(
self.predicate_ab,
PredicateFormula(PredicateSymbol("Predicate", 2),
Variable.fromString("a"),
Variable.fromString("c")))
self.assertNotEqual(
self.predicate_ab,
PredicateFormula(PredicateSymbol("Another_Predicate", 2),
Variable.fromString("a"),
Variable.fromString("c")))
self.assertNotEqual(
self.A_a,
PredicateFormula(PredicateSymbol("A", 1),
Variable.fromString("b")))
self.assertNotEqual(
self.b_equal_c,
Equal(Variable.fromString("b"), Variable.fromString("b")))
self.assertNotEqual(
self.neg_a_equal_a,
Not(Equal(Variable.fromString("b"), Variable.fromString("a"))))
self.assertNotEqual(
self.forall_b_exists_a_predicate_ab,
ForAll(
Variable.fromString("b"),
Exists(
Variable.fromString("a"),
PredicateFormula(PredicateSymbol("ANOTHER_PREDICATE", 2),
Variable.fromString("a"),
Variable.fromString("b")))))