def model_checking_ans():
not_p11 = model_checking.Formula("P11", True) # !P(1,1)
not_b11 = model_checking.Formula("B11", True) # !B(1,1)
b21_1 = model_checking.Formula("B21", True) # B(2,1)
conj_left_sub = model_checking.Conjunction(False, not_b11, b21_1)
conj_left = model_checking.Conjunction(False, not_p11, conj_left_sub) # !P(1,1) ^ !B(1,1) ^ B(2,1)
b11 = model_checking.Formula("B11")
p12 = model_checking.Formula("P12")
p21 = model_checking.Formula("P21")
disj_1 = model_checking.Disjunction(False, p12, p21)
bi_1 = model_checking.Biconditional(False, b11, disj_1) # B(1,1) <=> (P(1,2) V P(2,1))
b21_2 = model_checking.Formula("B21")
p11 = model_checking.Formula("P11")
p22 = model_checking.Formula("P22")
p31 = model_checking.Formula("P31")
disj_2 = model_checking.Disjunction(False, p22, p31)
disj_3 = model_checking.Disjunction(False, p11, disj_2)
bi_2 = model_checking.Biconditional(False, b21_2, disj_3) # B(2,1) <=> (P(1,1) V P(2,2) V P(3,1))
conj_right = model_checking.Conjunction(False, bi_1, bi_2)
conj_kb = model_checking.Conjunction(False, conj_left, conj_right) # Knowledge base
formula_query = model_checking.Formula("P12")
return model_checking.print_ans(conj_kb, formula_query)
def model_checking_ans2():
# A <=> X
a_1 = model_checking.Formula("A")
x_1 = model_checking.Formula("X")
bi_a = model_checking.Biconditional(False, a_1, x_1)
# H <=> ((G ^ H) => A)
h_1 = model_checking.Formula("H")
g_1 = model_checking.Formula("G")
h_2 = model_checking.Formula("H")
conj_1 = model_checking.Conjunction(False, g_1, h_2)
a_2 = model_checking.Formula("A")
imply_1 = model_checking.Implication(False, conj_1, a_2)
bi_h = model_checking.Biconditional(False, h_1, imply_1)
conj_left = model_checking.Conjunction(False, bi_a, bi_h)
# C <=> (A ^ ?)
c_1 = model_checking.Formula("C")
a_3 = model_checking.Formula("A")
unknown_1 = model_checking.Formula("Unknown 1")
conj_2 = model_checking.Conjunction(False, a_3, unknown_1)
bi_c = model_checking.Biconditional(False, c_1, conj_2)
# G <=> (C => ?)
g_2 = model_checking.Formula("G")
c_2 = model_checking.Formula("C")
unknown_2 = model_checking.Formula("Unknown 2")
imply_2 = model_checking.Implication(False, c_2, unknown_2)
bi_g = model_checking.Biconditional(False, g_2, imply_2)
conj_right = model_checking.Conjunction(False, bi_c, bi_g)
conj_kb = model_checking.Conjunction(False, conj_left,
conj_right) # Knowledge base
query_x = model_checking.Formula("X")
query_y = model_checking.Formula("Y")
query_z = model_checking.Formula("Z")
query_w = model_checking.Formula("W")
a1 = model_checking.print_ans(conj_kb, query_x)
a2 = model_checking.print_ans(conj_kb, query_y)
a3 = model_checking.print_ans(conj_kb, query_z)
a4 = model_checking.print_ans(conj_kb, query_w)
return [a1, a2, a3, a4]
def model_checking_ans():
# P
formula_p_1 = model_checking.Formula("P")
# P => Q
formula_p_2 = model_checking.Formula("P")
formula_q = model_checking.Formula("Q")
imply = model_checking.Implication(False, formula_p_2, formula_q)
# KB: {P, P => Q}
conj_kb = model_checking.Conjunction(False, formula_p_1, imply)
# Query: Q
formula_query = model_checking.Formula("Q")
return model_checking.print_ans(conj_kb, formula_query)
def model_checking_ans():
# MYTHICAL => IMMORTAL
myth = model_checking.Formula("MYTHICAL")
immortal_1 = model_checking.Formula("IMMORTAL")
imply_1 = model_checking.Implication(False, myth, immortal_1)
# !MYTHICAL => (!IMMORTAL ^ MAMMAL)
not_myth = model_checking.Formula("MYTHICAL", True)
not_immortal = model_checking.Formula("IMMORTAL", True)
mammal_1 = model_checking.Formula("MAMMAL")
conj_sub = model_checking.Conjunction(False, not_immortal, mammal_1)
imply_2 = model_checking.Implication(False, not_myth, conj_sub)
conj_left = model_checking.Conjunction(False, imply_1, imply_2)
# (IMMORTAL V MAMMAL) => HORNED
immortal_2 = model_checking.Formula("IMMORTAL")
mammal_2 = model_checking.Formula("MAMMAL")
disj_sub = model_checking.Disjunction(False, immortal_2, mammal_2)
horn_1 = model_checking.Formula("HORNED")
imply_3 = model_checking.Implication(False, disj_sub, horn_1)
# HORNED => MAGICAL
horn_2 = model_checking.Formula("HORNED")
magical = model_checking.Formula("MAGICAL")
imply_4 = model_checking.Implication(False, horn_2, magical)
conj_right = model_checking.Conjunction(False, imply_3, imply_4)
conj_kb = model_checking.Conjunction(False, conj_left,
conj_right) # Knowledge base
query_myth = model_checking.Formula("MYTHICAL")
query_magical = model_checking.Formula("MAGICAL")
query_horn = model_checking.Formula("HORNED")
a1 = model_checking.print_ans(conj_kb, query_myth)
a2 = model_checking.print_ans(conj_kb, query_magical)
a3 = model_checking.print_ans(conj_kb, query_horn)
return [a1, a2, a3]
def model_checking_ans1():
# A <=> X
a_1 = model_checking.Formula("A")
x_1 = model_checking.Formula("X")
bi_a = model_checking.Biconditional(False, a_1, x_1)
# B <=> (Y V Z)
b_1 = model_checking.Formula("B")
y_1 = model_checking.Formula("Y")
z_1 = model_checking.Formula("Z")
disj_1 = model_checking.Disjunction(False, y_1, z_1)
bi_b = model_checking.Biconditional(False, b_1, disj_1)
conj_ab = model_checking.Conjunction(False, bi_a, bi_b)
# C <=> (A ^ B)
c_1 = model_checking.Formula("C")
a_2 = model_checking.Formula("A")
b_2 = model_checking.Formula("B")
conj_1 = model_checking.Conjunction(False, a_2, b_2)
bi_c = model_checking.Biconditional(False, c_1, conj_1)
# D <=> (X ^ Y)
d_1 = model_checking.Formula("D")
x_2 = model_checking.Formula("X")
y_2 = model_checking.Formula("Y")
conj_2 = model_checking.Conjunction(False, x_2, y_2)
bi_d = model_checking.Biconditional(False, d_1, conj_2)
conj_cd = model_checking.Conjunction(False, bi_c, bi_d)
conj_abcd = model_checking.Conjunction(False, conj_ab, conj_cd)
# E <=> (X ^ Z)
e_1 = model_checking.Formula("E")
x_3 = model_checking.Formula("X")
z_2 = model_checking.Formula("Z")
conj_3 = model_checking.Conjunction(False, x_3, z_2)
bi_e = model_checking.Biconditional(False, e_1, conj_3)
# F <=> (D V E)
f_1 = model_checking.Formula("F")
d_2 = model_checking.Formula("D")
e_2 = model_checking.Formula("E")
disj_2 = model_checking.Disjunction(False, d_2, e_2)
bi_f = model_checking.Biconditional(False, f_1, disj_2)
conj_ef = model_checking.Conjunction(False, bi_e, bi_f)
# G <=> (C => F)
g_1 = model_checking.Formula("G")
c_2 = model_checking.Formula("C")
f_2 = model_checking.Formula("F")
imply_1 = model_checking.Implication(False, c_2, f_2)
bi_g = model_checking.Biconditional(False, g_1, imply_1)
# H <=> ((G ^ H) => A)
h_1 = model_checking.Formula("H")
g_2 = model_checking.Formula("G")
h_2 = model_checking.Formula("H")
conj_4 = model_checking.Conjunction(False, g_2, h_2)
a_3 = model_checking.Formula("A")
imply_2 = model_checking.Implication(False, conj_4, a_3)
bi_h = model_checking.Biconditional(False, h_1, imply_2)
conj_gh = model_checking.Conjunction(False, bi_g, bi_h)
conj_efgh = model_checking.Conjunction(False, conj_ef, conj_gh)
conj_kb = model_checking.Conjunction(False, conj_abcd,
conj_efgh) # Knowledge base
query_x = model_checking.Formula("X")
query_y = model_checking.Formula("Y")
query_z = model_checking.Formula("Z")
query_w = model_checking.Formula("W")
a1 = model_checking.print_ans(conj_kb, query_x)
a2 = model_checking.print_ans(conj_kb, query_y)
a3 = model_checking.print_ans(conj_kb, query_z)
a4 = model_checking.print_ans(conj_kb, query_w)
return [a1, a2, a3, a4]