def ghostDirectionSuccessorStateAxioms(t, ghost_num, blocked_west_positions,
blocked_east_positions):
"""
Successor state axiom for patrolling ghost direction state (t) (from t-1).
west or east walls.
Current <==> (causes to stay) | (causes of current)
"""
pos_str = ghost_pos_str + str(ghost_num)
east_str = ghost_east_str + str(ghost_num)
west_positions = list()
east_positions = list()
blocked_west_positions_copy = blocked_west_positions[:]
blocked_east_positions_copy = blocked_east_positions[:]
while blocked_west_positions_copy:
position = blocked_west_positions_copy.pop()
west_positions.append(
logic.PropSymbolExpr(pos_str, position[0], position[1], t))
while blocked_east_positions_copy:
position = blocked_east_positions_copy.pop()
east_positions.append(
logic.PropSymbolExpr(pos_str, position[0], position[1], t))
west_positions = logic.disjoin(west_positions)
east_positions = logic.disjoin(east_positions)
conditions = (west_positions & ~logic.PropSymbolExpr(east_str, t - 1)) | (
~east_positions & logic.PropSymbolExpr(east_str, t - 1))
final_axiom = logic.PropSymbolExpr(east_str, t) % conditions
return final_axiom
def ghostDirectionSuccessorStateAxioms(t, ghost_num, blocked_west_positions,
blocked_east_positions):
"""
Successor state axiom for patrolling ghost direction state (t) (from t-1).
west or east walls.
Current <==> (causes to stay) | (causes of current)
"""
pos_str = ghost_pos_str + str(ghost_num)
east_str = ghost_east_str + str(ghost_num)
"*** YOUR CODE HERE ***"
west_action = ~(logic.PropSymbolExpr(east_str, t - 1))
east_action = logic.PropSymbolExpr(east_str, t - 1)
west_list = []
east_list = []
for pos in blocked_east_positions:
x, y = pos
not_blocked_east = ~logic.PropSymbolExpr(pos_str, x, y, t)
lst = logic.conjoin(east_action, not_blocked_east)
east_list.append(lst)
for pos in blocked_west_positions:
x, y = pos
blocked_west = logic.PropSymbolExpr(pos_str, x, y, t)
lst = logic.conjoin(west_action, blocked_west)
west_list.append(lst)
east_list = logic.conjoin(east_list)
west_list = logic.disjoin(west_list)
return logic.PropSymbolExpr(east_str, t) % logic.disjoin(
east_list, west_list)
def exactlyOne(literals):
"""
Given a list of logic.Expr literals, return a single logic.Expr instance in
CNF (conjunctive normal form)that represents the logic that exactly one of
the expressions in the list is true.
"""
# print literals
conjunctions = []
one_must_be_true_list = []
for literal in literals:
not_literal = ~literal
one_must_be_true_list.append(literal)
# Disjoin literal with NOT(literal) for every other element besides this literal
# and add it to the list to be conjoined
reached_literal = False
for inner_literal in literals:
if (reached_literal):
not_inner_literal = ~inner_literal
disjunction = logic.disjoin(not_literal, not_inner_literal)
conjunctions.append(disjunction)
if literal == inner_literal:
reached_literal = True
# Add the expression that states at least one of the literals must be true
one_must_be_true = logic.disjoin(one_must_be_true_list)
conjunctions.append(one_must_be_true)
return logic.conjoin(conjunctions)
def SLAMSensorAxioms(t, non_outer_wall_coords):
all_percept_exprs = []
combo_var_def_exprs = []
for direction in DIRECTIONS:
percept_exprs = []
dx, dy = DIR_TO_DXDY_MAP[direction]
for x, y in non_outer_wall_coords:
combo_var = PropSymbolExpr(pacman_wall_str, x, y, t, x + dx,
y + dy)
percept_exprs.append(combo_var)
combo_var_def_exprs.append(
combo_var % (PropSymbolExpr(pacman_str, x, y, t)
& PropSymbolExpr(wall_str, x + dx, y + dy)))
blocked_dir_clause = PropSymbolExpr(blocked_str_map[direction], t)
all_percept_exprs.append(blocked_dir_clause % disjoin(percept_exprs))
percept_to_blocked_sent = []
for n in range(1, 4):
wall_combos_size_n = itertools.combinations(blocked_str_map.values(),
n)
n_walls_blocked_sent = disjoin([
conjoin(
[PropSymbolExpr(blocked_str, t) for blocked_str in wall_combo])
for wall_combo in wall_combos_size_n
])
# n_walls_blocked_sent is of form: (N & S) | (N & E) | ...
percept_to_blocked_sent.append(
PropSymbolExpr(geq_num_adj_wall_str_map[n], t) %
n_walls_blocked_sent)
return conjoin(all_percept_exprs + combo_var_def_exprs +
percept_to_blocked_sent)
def exactlyOne(literals):
"""
Given a list of logic.Expr literals, return a single logic.Expr instance in
CNF (conjunctive normal form)that represents the logic that exactly one of
the inits in the list is true.
"""
"*** YOUR CODE HERE ***"
conjunctions = []
true_list = []
for literal in literals:
true_list.append(literal)
reached = False
for inner_literal in literals:
if reached:
not_inner_literal = ~inner_literal
disjunction = logic.disjoin(~literal, not_inner_literal)
conjunctions.append(disjunction)
if literal == inner_literal:
reached = True
true_one = logic.disjoin(true_list)
conjunctions.append(true_one)
return logic.conjoin(conjunctions)
def sentence1():
"""Returns a Expr instance that encodes that the following expressions are all true.
A or B
(not A) if and only if ((not B) or C)
(not A) or (not B) or C
"""
s1 = disjoin(A, B)
s2 = ~A % disjoin(~B, C)
s3 = disjoin(~A, ~B, C)
return conjoin(s1, s2, s3)
def pacmanSLAMSuccessorStateAxioms(x, y, t, walls_grid, var_str=pacman_str):
"""
Similar to `pacmanSuccessorStateAxioms` but accounts for illegal actions
where the pacman might not move timestep to timestep.
Available actions are ['North', 'East', 'South', 'West']
"""
moved_tm1_possibilities = []
if not walls_grid[x][y + 1]:
moved_tm1_possibilities.append(
PropSymbolExpr(var_str, x, y + 1, t - 1)
& PropSymbolExpr('South', t - 1))
if not walls_grid[x][y - 1]:
moved_tm1_possibilities.append(
PropSymbolExpr(var_str, x, y - 1, t - 1)
& PropSymbolExpr('North', t - 1))
if not walls_grid[x + 1][y]:
moved_tm1_possibilities.append(
PropSymbolExpr(var_str, x + 1, y, t - 1)
& PropSymbolExpr('West', t - 1))
if not walls_grid[x - 1][y]:
moved_tm1_possibilities.append(
PropSymbolExpr(var_str, x - 1, y, t - 1)
& PropSymbolExpr('East', t - 1))
if not moved_tm1_possibilities:
return None
moved_tm1_sent = conjoin([
~PropSymbolExpr(var_str, x, y, t - 1), ~PropSymbolExpr(wall_str, x, y),
disjoin(moved_tm1_possibilities)
])
unmoved_tm1_possibilities_aux_exprs = [] # merged variables
aux_expr_defs = []
for direction in DIRECTIONS:
dx, dy = DIR_TO_DXDY_MAP[direction]
wall_dir_clause = PropSymbolExpr(
wall_str, x + dx, y + dy) & PropSymbolExpr(direction, t - 1)
wall_dir_combined_literal = PropSymbolExpr(wall_str + direction,
x + dx, y + dy, t - 1)
unmoved_tm1_possibilities_aux_exprs.append(wall_dir_combined_literal)
aux_expr_defs.append(wall_dir_combined_literal % wall_dir_clause)
unmoved_tm1_sent = conjoin([
PropSymbolExpr(var_str, x, y, t - 1),
disjoin(unmoved_tm1_possibilities_aux_exprs)
])
return conjoin([
PropSymbolExpr(var_str, x, y, t) %
disjoin([moved_tm1_sent, unmoved_tm1_sent])
] + aux_expr_defs)
def sentence1():
"""Returns a logic.Expr instance that encodes that the following expressions are all true.
A or B
(not A) if and only if ((not B) or C)
(not A) or (not B) or C
"""
"*** YOUR CODE HERE ***"
ans1 = logic.Expr('A') | logic.Expr('B')
ans2 = ~logic.Expr('A') % logic.disjoin(
[~logic.Expr('B'), logic.Expr('C')])
ans3 = logic.disjoin([~logic.Expr('A'), ~logic.Expr('B'), logic.Expr('C')])
return logic.conjoin([ans1, ans2, ans3])
def sentence1():
"""Returns a Expr instance that encodes that the following expressions are all true.
A or B
(not A) if and only if ((not B) or C)
(not A) or (not B) or C
"""
"*** BEGIN YOUR CODE HERE ***"
A = Expr('A')
B = Expr('B')
C = Expr('C')
return conjoin(disjoin(A, B), ~A % disjoin(~B, C), disjoin(~A, ~B, C))
"*** END YOUR CODE HERE ***"
def sentence1():
"""Returns a logic.Expr instance that encodes that the following expressions are all true.
A or B
(not A) if and only if ((not B) or C)
(not A) or (not B) or C
"""
A = logic.Expr('A')
B = logic.Expr('B')
C = logic.Expr('C')
aaa = logic.disjoin(A, B)
a_or_b = ~A % (~B | C)
not_a = logic.disjoin(~A, ~B, C)
return logic.conjoin(aaa, a_or_b, not_a)
def sentence2():
"""Returns a logic.Expr instance that encodes that the following expressions are all true.
C if and only if (B or D)
A implies ((not B) and (not D))
(not (B and (not C))) implies A
(not D) implies C
"""
"*** YOUR CODE HERE ***"
A = logic.Expr('A')
B = logic.Expr('B')
C = logic.Expr('C')
D = logic.Expr('D')
notB = ~B
notD = ~D
notC = ~C
B_or_D = logic.disjoin((B), (D))
notB_and_notD = logic.conjoin((notB), (notD))
C_iff_B_or_D = C % B_or_D
A_implies_notB_and_notD = A >> notB_and_notD
B_and_notC = logic.conjoin((B), (notC))
not_B_and_notC_implies_A = ~B_and_notC >> A
notD_implies_C = notD >> C
return logic.conjoin((C_iff_B_or_D), (A_implies_notB_and_notD),
(not_B_and_notC_implies_A), (notD_implies_C))
def exactlyOne(literals) :
"""
Given a list of logic.Expr literals, return a single logic.Expr instance in
CNF (conjunctive normal form)that represents the logic that exactly one of
the expressions in the list is true.
"""
"*** YOUR CODE HERE ***"
n = len(literals)
clause_brev = []
clauses = []
for i in range(2**n):
bstr = str(bin(i))
clause_brev.append(bstr[2:].zfill(n))
for brev in clause_brev:
clause = []
if (bin(int(brev,2)).count('1') == 1):
continue
for i in range(n):
if (brev[i] == '1'):
clause.append(~literals[i])
elif (brev[i] == '0'):
clause.append(literals[i])
temp=clause[0]
for i in range(n-1):
temp = logic.disjoin(temp,clause[i+1])
clauses.append(temp)
expression = clauses[0]
for i in range(2**n-n-1):
expression = logic.conjoin(expression,clauses[i+1])
return expression
def atLeastOne(literals) :
"""
Given a list of logic.Expr literals (i.e. in the form A or ~A), return a single
logic.Expr instance in CNF (conjunctive normal form) that represents the logic
that at least one of the literals in the list is true.
>>> A = logic.PropSymbolExpr('A');
>>> B = logic.PropSymbolExpr('B');
>>> symbols = [A, B]
>>> atleast1 = atLeastOne(symbols)
>>> model1 = {A:False, B:False}
>>> print logic.pl_true(atleast1,model1)
False
>>> model2 = {A:False, B:True}
>>> print logic.pl_true(atleast1,model2)
True
>>> model3 = {A:True, B:True}
>>> print logic.pl_true(atleast1,model2)
True
"""
"*** YOUR CODE HERE ***"
expression = literals[0]
for i in range(len(literals)-1):
expression = logic.disjoin(expression, literals[i+1])
return expression
def sentence1():
"""Returns a logic.Expr instance that encodes that the following expressions are all true.
A or B
(not A) if and only if ((not B) or C)
(not A) or (not B) or C
"""
"*** YOUR CODE HERE ***"
A = logic.Expr("A")
B = logic.Expr("B")
C = logic.Expr("C")
first = logic.disjoin(A, B)
second = (~A) % logic.disjoin(~B, C)
third = logic.disjoin(~A, ~B, C)
return logic.conjoin(first, second, third)
def pacmanAliveSuccessorStateAxioms(x, y, t, num_ghosts):
"""
Successor state axiom for patrolling ghost state (x,y,t) (from t-1).
Current <==> (causes to stay) | (causes of current)
"""
ghost_strs = [
ghost_pos_str + str(ghost_num) for ghost_num in xrange(num_ghosts)
]
current = logic.PropSymbolExpr(pacman_str, x, y, t)
ghosts = ghost_strs[:]
neighbors = []
k = []
l = []
while num_ghosts != 0:
k += [
logic.PropSymbolExpr(ghost_strs[num_ghosts - 1], x, y, t - 1)
| logic.PropSymbolExpr(ghost_strs[num_ghosts - 1], x, y, t)
]
num_ghosts -= 1
m = ~logic.PropSymbolExpr(pacman_alive_str, t - 1)
prev_states = logic.disjoin(k)
prev_states = logic.conjoin(logic.PropSymbolExpr(pacman_str, x, y, t),
prev_states) | m
final_axiom = ~logic.PropSymbolExpr(pacman_alive_str, t) % prev_states
return final_axiom
def ghostPositionSuccessorStateAxioms(x, y, t, ghost_num, walls_grid):
"""
Successor state axiom for patrolling ghost state (x,y,t) (from t-1).
Current <==> (causes to stay) | (causes of current)
GE is going east, ~GE is going west
"""
pos_str = ghost_pos_str+str(ghost_num)
east_str = ghost_east_str+str(ghost_num)
pos = logic.PropSymbolExpr(pos_str, x, y, t)
listAdj = [(x-1, y), (x+1, y)]
lst = []
for l in listAdj:
if not walls_grid[l[0]][l[1]]:
if l == (x-1, y):
e = logic.conjoin([logic.PropSymbolExpr(pos_str, x-1, y, t-1), logic.PropSymbolExpr(east_str, t-1)])
else:
e = logic.conjoin([logic.PropSymbolExpr(pos_str, x+1, y, t-1), ~(logic.PropSymbolExpr(east_str, t-1))])
lst.append(e)
if walls_grid[x-1][y] & walls_grid[x+1][y]: #if there are walls on both sides and ghost cannot move
lst.append(logic.PropSymbolExpr(pos_str, x, y, t-1))
if (len(lst) == 0):
return pos % pos
r = logic.disjoin(lst)
return pos % r
def ghostPositionSuccessorStateAxioms(x, y, t, ghost_num, walls_grid):
"""
Successor state axiom for patrolling ghost state (x,y,t) (from t-1).
Current <==> (causes to stay) | (causes of current)
GE is going east, ~GE is going west
"""
pos_str = ghost_pos_str+str(ghost_num)
east_str = ghost_east_str+str(ghost_num)
pos = logic.PropSymbolExpr(pos_str, x, y, t)
listAdj = [(x-1, y), (x+1, y)]
lst = []
for l in listAdj:
if not walls_grid[l[0]][l[1]]:
if l == (x-1, y):
e = logic.conjoin([logic.PropSymbolExpr(pacman_str, x-1, y, t-1), logic.PropSymbolExpr(east_str, t-1)])
else:
e = logic.conjoin([logic.PropSymbolExpr(pacman_str, x+1, y, t-1), ~(logic.PropSymbolExpr(east_str, t-1))])
lst.append(e)
if (len(lst) == 0):
return pos % pos
r = logic.disjoin(lst)
return pos % r
"*** YOUR CODE HERE ***"
return logic.Expr('A') # Replace this with your expression
def pacmanSuccessorStateAxioms(x, y, t, walls_grid):
"""
Successor state axiom for state (x,y,t) (from t-1), given the board (as a
grid representing the wall locations).
Current <==> (previous position at time t-1) & (took action to move to x, y)
"""
"*** YOUR CODE HERE ***"
current_pos = logic.PropSymbolExpr(pacman_str, x, y, t)
pre = []
if not walls_grid[x][y - 1]:
pre_pos = logic.PropSymbolExpr(pacman_str, x, y - 1, t - 1)
move = logic.PropSymbolExpr("North", t - 1)
pre.append(move & pre_pos)
if not walls_grid[x][y + 1]:
pre_pos = logic.PropSymbolExpr(pacman_str, x, y + 1, t - 1)
move = logic.PropSymbolExpr("South", t - 1)
pre.append(move & pre_pos)
if not walls_grid[x - 1][y]:
pre_pos = logic.PropSymbolExpr(pacman_str, x - 1, y, t - 1)
move = logic.PropSymbolExpr("East", t - 1)
pre.append(move & pre_pos)
if not walls_grid[x + 1][y]:
pre_pos = logic.PropSymbolExpr(pacman_str, x + 1, y, t - 1)
move = logic.PropSymbolExpr("West", t - 1)
pre.append(move & pre_pos)
all_pre = logic.disjoin(pre)
return current_pos % all_pre
def atLeastOne(literals):
"""
Given a list of Expr literals (i.e. in the form A or ~A), return a single
Expr instance in CNF (conjunctive normal form) that represents the logic
that at least one of the literals in the list is true.
>>> A = PropSymbolExpr('A');
>>> B = PropSymbolExpr('B');
>>> symbols = [A, B]
>>> atleast1 = atLeastOne(symbols)
>>> model1 = {A:False, B:False}
>>> print(pl_true(atleast1,model1))
False
>>> model2 = {A:False, B:True}
>>> print(pl_true(atleast1,model2))
True
>>> model3 = {A:True, B:True}
>>> print(pl_true(atleast1,model2))
True
"""
"*** BEGIN YOUR CODE HERE ***"
conj = literals[0]
for i in literals[1:]:
conj = disjoin(conj, i)
return conj
"*** END YOUR CODE HERE ***"
def pacmanSuccessorStateAxioms(x, y, t, walls_grid):
"""
Successor state axiom for state (x,y,t) (from t-1), given the board (as a
grid representing the wall locations).
Current <==> (previous position at time t-1) & (took action to move to x, y)
"""
"*** YOUR CODE HERE ***"
def noWallHere(coord):
return not walls_grid[coord[0]][coord[1]]
listPrev = []
directions = ["East", "West", "South", "North"]
at = [(x - 1, y), (x + 1, y), (x, y + 1), (x, y - 1)]
for i in xrange(len(directions)):
direc = directions[i]
coord = at[i]
if noWallHere(coord):
prevAtHere = logic.PropSymbolExpr(pacman_str, coord[0], coord[1],
t - 1)
prevGoThere = logic.PropSymbolExpr(direc, t - 1)
listPrev.append(logic.conjoin(prevAtHere, prevGoThere))
pacmanNow = logic.PropSymbolExpr(pacman_str, x, y, t)
return pacmanNow % logic.disjoin(i for i in listPrev)
def pacmanSuccessorStateAxioms(x, y, t, walls_grid):
"""
Successor state axiom for state (x,y,t) (from t-1), given the board (as a
grid representing the wall locations).
Current <==> (previous position at time t-1) & (took action to move to x, y)
"""
moves = []
if not walls_grid[x + 1][y]:
moves.append(
logic.PropSymbolExpr(pacman_str, x + 1, y, t - 1)
& logic.PropSymbolExpr('West', t - 1))
if not walls_grid[x - 1][y]:
moves.append(
logic.PropSymbolExpr(pacman_str, x - 1, y, t - 1)
& logic.PropSymbolExpr('East', t - 1))
if not walls_grid[x][y + 1]:
moves.append(
logic.PropSymbolExpr(pacman_str, x, y + 1, t - 1)
& logic.PropSymbolExpr('South', t - 1))
if not walls_grid[x][y - 1]:
moves.append(
logic.PropSymbolExpr(pacman_str, x, y - 1, t - 1)
& logic.PropSymbolExpr('North', t - 1))
return logic.PropSymbolExpr(pacman_str, x, y, t) % (logic.disjoin(moves))
def atLeastOne(literals):
"""
Given a list of logic.Expr literals (i.e. in the form A or ~A), return a single
logic.Expr instance in CNF (conjunctive normal form) that represents the logic
that at least one of the literals in the list is true.
>>> A = logic.PropSymbolExpr('A');
>>> B = logic.PropSymbolExpr('B');
>>> symbols = [A, B]
>>> atleast1 = atLeastOne(symbols)
>>> model1 = {A:False, B:False}
>>> print logic.pl_true(atleast1,model1)
False
>>> model2 = {A:False, B:True}
>>> print logic.pl_true(atleast1,model2)
True
>>> model3 = {A:True, B:True}
>>> print logic.pl_true(atleast1,model2)
True
"""
"*** YOUR CODE HERE ***"
# symbols=list(combinations(literals,2))
y = logic.disjoin(literals)
# print(symbols)
# for i in symbols:
# x=logic.conjoin(i)
# y=logic.disjoin(y,x)
return y
util.raiseNotDefined()
def sentence1():
"""Returns a logic.Expr instance that encodes that the following expressions are all true.
A or B
(not A) if and only if ((not B) or C)
(not A) or (not B) or C
"""
"*** YOUR CODE HERE ***"
A = logic.Expr('A')
B = logic.Expr('B')
C = logic.Expr('C')
A_or_B = logic.disjoin(A, B)
Two = ~A % logic.disjoin(~B, C)
Three = logic.disjoin(~A, ~B, C)
return logic.conjoin(A_or_B, Two, Three)
util.raiseNotDefined()
def ghostPositionSuccessorStateAxioms(x, y, t, ghost_num, walls_grid):
"""
Successor state axiom for patrolling ghost state (x,y,t) (from t-1).
Current <==> (causes to stay) | (causes of current)
GE is going east, ~GE is going west
"""
pos_str = ghost_pos_str + str(ghost_num)
east_str = ghost_east_str + str(ghost_num)
"*** YOUR CODE HERE ***"
left = walls_grid[x - 1][y]
right = walls_grid[x + 1][y]
possible_locations = []
left_prev = logic.PropSymbolExpr(pos_str, x - 1, y, t - 1)
right_prev = logic.PropSymbolExpr(pos_str, x + 1, y, t - 1)
west_action = ~(logic.PropSymbolExpr(east_str, t - 1))
east_action = logic.PropSymbolExpr(east_str, t - 1)
if left and right:
return logic.PropSymbolExpr(pos_str, x, y, t) % logic.PropSymbolExpr(
pos_str, x, y, t - 1)
if not left:
possible_locations.append(logic.conjoin(left_prev, east_action))
if not right:
possible_locations.append(logic.conjoin(right_prev, west_action))
return logic.PropSymbolExpr(pos_str, x, y,
t) % logic.disjoin(possible_locations)
def pacmanSuccessorStateAxioms(x, y, t, walls_grid, var_str=pacman_str):
"""
Successor state axiom for state (x,y,t) (from t-1), given the board (as a
grid representing the wall locations).
Current <==> (previous position at time t-1) & (took action to move to x, y)
Available actions are ['North', 'East', 'South', 'West']
Note that STOP is not an available action.
"""
possibilities = []
if not walls_grid[x][y + 1]:
possibilities.append(
PropSymbolExpr(var_str, x, y + 1, t - 1)
& PropSymbolExpr('South', t - 1))
if not walls_grid[x][y - 1]:
possibilities.append(
PropSymbolExpr(var_str, x, y - 1, t - 1)
& PropSymbolExpr('North', t - 1))
if not walls_grid[x + 1][y]:
possibilities.append(
PropSymbolExpr(var_str, x + 1, y, t - 1)
& PropSymbolExpr('West', t - 1))
if not walls_grid[x - 1][y]:
possibilities.append(
PropSymbolExpr(var_str, x - 1, y, t - 1)
& PropSymbolExpr('East', t - 1))
if not possibilities:
return None
return PropSymbolExpr(var_str, x, y, t) % disjoin(possibilities)
def sentence3():
"""Using the symbols WumpusAlive[1], WumpusAlive[0], WumpusBorn[0], and WumpusKilled[0],
created using the logic.PropSymbolExpr constructor, return a logic.PropSymbolExpr
instance that encodes the following English sentences (in this order):
The Wumpus is alive at time 1 if and only if the Wumpus was alive at time 0 and it was
not killed at time 0 or it was not alive and time 0 and it was born at time 0.
The Wumpus cannot both be alive at time 0 and be born at time 0.
The Wumpus is born at time 0.
"""
"*** YOUR CODE HERE ***"
#know the use of the PropSymbolExpr from logic.py
Alive_1 = logic.PropSymbolExpr("WumpusAlive", 1)
#print (Alive_1)
Alive_0 = logic.PropSymbolExpr("WumpusAlive", 0)
Born_0 = logic.PropSymbolExpr("WumpusBorn", 0)
Killed_0 = logic.PropSymbolExpr("WumpusKilled", 0)
One = Alive_1 % logic.disjoin(logic.conjoin(Alive_0, ~Killed_0),
logic.conjoin(~Alive_0, Born_0))
Two = ~logic.conjoin(Alive_0, Born_0)
Three = Born_0
return logic.conjoin(One, Two, Three)
util.raiseNotDefined()
def pacmanSuccessorStateAxioms(x, y, t, walls_grid):
"""
Successor state axiom for state (x,y,t) (from t-1), given the board (as a
grid representing the wall locations).
Current <==> (previous position at time t-1) & (took action to move to x, y)
"""
"*** YOUR CODE HERE ***"
expr = []
if (not walls_grid[x][y - 1]):
expr += [
logic.PropSymbolExpr(pacman_str, x, y - 1, t - 1)
& logic.PropSymbolExpr('North', t - 1)
]
if (not walls_grid[x][y + 1]):
expr += [
logic.PropSymbolExpr(pacman_str, x, y + 1, t - 1)
& logic.PropSymbolExpr('South', t - 1)
]
if (not walls_grid[x - 1][y]):
expr += [
logic.PropSymbolExpr(pacman_str, x - 1, y, t - 1)
& logic.PropSymbolExpr('East', t - 1)
]
if (not walls_grid[x + 1][y]):
expr += [
logic.PropSymbolExpr(pacman_str, x + 1, y, t - 1)
& logic.PropSymbolExpr('West', t - 1)
]
return logic.PropSymbolExpr(pacman_str, x, y, t) % logic.disjoin(
expr) # Replace this with your expression
def pacmanSuccessorStateAxioms(x, y, t, walls_grid):
"""
Successor state axiom for state (x,y,t) (from t-1), given the board (as a
grid representing the wall locations).
Current <==> (previous position at time t-1) & (took action to move to x, y)
"""
"*** YOUR CODE HERE ***"
# init current/final position
current = logic.PropSymbolExpr(pacman_str, x, y, t)
test = []
if walls_grid[x+1][y] != True:
action = logic.PropSymbolExpr(pacman_str, x+1, y, t-1) & logic.PropSymbolExpr('West', t-1)
test.append(action)
successor_nodes.append((x+1, y, t))
if walls_grid[x-1][y] != True:
action2 = logic.PropSymbolExpr(pacman_str, x-1, y, t-1) & logic.PropSymbolExpr('East', t-1)
test.append(action2)
successor_nodes.append((x+1, y, t))
if walls_grid[x][y+1] != True:
action3 = logic.PropSymbolExpr(pacman_str, x, y+1, t-1) & logic.PropSymbolExpr('South', t-1)
test.append(action3)
successor_nodes.append((x+1, y, t))
if walls_grid[x][y-1] != True:
action4 = logic.PropSymbolExpr(pacman_str, x, y-1, t-1) & logic.PropSymbolExpr('North', t-1)
test.append(action4)
successor_nodes.append((x+1, y, t))
return current % logic.disjoin(test)
def sentence1():
"""Returns a logic.Expr instance that encodes that the following expressions are all true.
A or B
(not A) if and only if ((not B) or C)
(not A) or (not B) or C
"""
"*** YOUR CODE HERE ***"
a = logic.Expr('A')
B = logic.Expr('B')
C = logic.Expr('C')
sentence1 = logic.disjoin(a,B)
sentence2 = logic.disjoin(~a%(~B|C))
sentence3 = logic.disjoin(~a,~B,C)
return logic.conjoin(sentence1,sentence2,sentence3)
util.raiseNotDefined()
def exactlyOne(literals):
"""
Given a list of logic.Expr literals, return a single logic.Expr instance in
CNF (conjunctive normal form)that represents the logic that exactly one of
the expressions in the list is true.
"""
"*** YOUR CODE HERE ***"
result = []
for value in literals:
for other in literals:
if (other != value):
result.append(logic.disjoin(~value, ~other))
result.append(logic.disjoin(literals))
return logic.conjoin(result)
def exactlyOne(literals):
"""
Given a list of logic.Expr literals, return a single logic.Expr instance in
CNF (conjunctive normal form)that represents the logic that exactly one of
the expressions in the list is true.
"""
conj_list = []
for literal in literals: # could set a variable to indicate if reach the result, to remove repetitive pair
for pair_literal in literals:
if literal != pair_literal:
pair = logic.disjoin(~literal, ~pair_literal)
conj_list.append(pair)
at_least_one = logic.disjoin(literals)
conj_list.append(at_least_one)
return logic.conjoin(conj_list)
def exactlyOne(literals) :
"""
Given a list of logic.Expr literals, return a single logic.Expr instance in
CNF (conjunctive normal form)that represents the logic that exactly one of
the expressions in the list is true.
"""
if len(literals) == 1:
return literals[0]
return logic.conjoin([logic.disjoin(literals),atMostOne(literals)])
def sentence1():
"""Returns a logic.Expr instance that encodes that the following expressions are all true.
A or B
(not A) if and only if ((not B) or C)
(not A) or (not B) or C
"""
"*** YOUR CODE HERE ***"
A, B, C = logic.Expr('A'), logic.Expr('B'), logic.Expr('C')
line1, line2, line3 = A | B, ~A % (~B | C), logic.disjoin(~A, ~B, C)
return logic.conjoin(line1, line2, line3)
def ghostDirectionSuccessorStateAxioms(t, ghost_num, blocked_west_positions, blocked_east_positions):
"""
Successor state axiom for patrolling ghost direction state (t) (from t-1).
west or east walls.
Current <==> (causes to stay) | (causes of current)
"""
# iterate over
# blocked east and blocked west disjoin
pos_str = ghost_pos_str+str(ghost_num)
east_str = ghost_east_str+str(ghost_num)
lst = []
lst3 = []
for (x, y) in blocked_east_positions:
lst.append(logic.PropSymbolExpr(pos_str, x, y, t))
east = ~(logic.disjoin(lst))
east = logic.PropSymbolExpr(east_str, t-1) & east
lst2 = []
for (x, y) in blocked_west_positions:
lst2.append(logic.PropSymbolExpr(pos_str, x, y, t))
west = logic.disjoin(lst2)
west = ~(logic.PropSymbolExpr(east_str, t-1)) & west
return logic.PropSymbolExpr(east_str, t) % (east | west)
def atMostOne(literals) :
"""
Given a list of logic.Expr literals, return a single logic.Expr instance in
CNF (conjunctive normal form) that represents the logic that at most one of
the expressions in the list is true.
"""
notliterals = [~literal for literal in literals]
clauses = []
for i in range(0,len(literals)-1):
for j in range(i+1, len(literals)):
clause = [notliterals[i]] + [notliterals[j]]
clauses.append(logic.disjoin(clause))
return logic.conjoin(clauses)
def sentence1():
"""Returns a logic.Expr instance that encodes that the following expressions are all true.
A or B
(not A) if and only if ((not B) or C)
(not A) or (not B) or C
"""
A = logic.Expr('A')
B = logic.Expr('B')
C = logic.Expr('C')
expr1 = A | B
expr2 = (~A) % ((~B)|C)
expr3 = logic.disjoin([~A,~B,C])
return logic.conjoin([expr1,expr2,expr3])
def pacmanSuccessorStateAxioms(x, y, t, walls_grid):
"""
Successor state axiom for state (x,y,t) (from t-1), given the board (as a
grid representing the wall locations).
Current <==> (previous position at time t-1) & (took action to move to x, y)
"""
"*** YOUR CODE HERE ***"
lst = []
for i in [(-1, 0, "East"), (1, 0, "West"), (0, -1, "North"), (0, 1, "South")]:
xt, yt = x + i[0], y + i[1]
if not walls_grid[xt][yt]:
lst.append(logic.PropSymbolExpr(pacman_str, xt, yt, t - 1) & logic.PropSymbolExpr(i[2], t - 1))
if lst:
return logic.PropSymbolExpr(pacman_str, x, y, t) % logic.disjoin(lst)
else:
return logic.PropSymbolExpr(pacman_str, x, y, t) % logic.PropSymbolExpr(pacman_str, x, y, t - 1)
def ghostPositionSuccessorStateAxioms(x, y, t, ghost_num, walls_grid):
"""
Successor state axiom for patrolling ghost state (x,y,t) (from t-1).
Current <==> (causes to stay) | (causes of current)
GE is going east, ~GE is going west
"""
pos_str = ghost_pos_str+str(ghost_num)
east_str = ghost_east_str+str(ghost_num)
disjoin = []
if not walls_grid[x-1][y]:
disjoin.append(logic.PropSymbolExpr(pos_str,x - 1,y, t-1) & logic.PropSymbolExpr(east_str,t-1))
if not walls_grid[x+1][y]:
disjoin.append(logic.PropSymbolExpr(pos_str,x + 1,y, t-1) & ~logic.PropSymbolExpr(east_str,t-1))
if walls_grid[x-1][y] and walls_grid[x+1][y]:
disjoin.append(logic.PropSymbolExpr(pos_str, x, y, t-1))
disjoin = logic.disjoin(disjoin)
return logic.to_cnf(~logic.PropSymbolExpr(pos_str, x, y, t) | disjoin) & logic.to_cnf(~disjoin|logic.PropSymbolExpr(pos_str, x, y, t))
def sentence2():
"""Returns a logic.Expr instance that encodes that the following expressions are all true.
C if and only if (B or D)
A implies ((not B) and (not D))
(not (B and (not C))) implies A
(not D) implies C
"""
"*** YOUR CODE HERE ***"
A, B, C, D = logic.Expr('A'), logic.Expr('B'), logic.Expr('C'), logic.Expr('D')
C_iff = C % logic.disjoin([B,D])
A_imp = A >> logic.conjoin([~B, ~D])
nots = ~(logic.conjoin([B, ~C])) >> A
notD = ~D >> C
return logic.conjoin([C_iff, A_imp, nots, notD])
util.raiseNotDefined()
def pacmanSuccessorStateAxioms(x, y, t, walls_grid):
"""
Successor state axiom for state (x,y,t) (from t-1), given the board (as a
grid representing the wall locations).
Current <==> (previous position at time t-1) & (took action to move to x, y)
"""
literals = []
if not walls_grid[x][y + 1]:
literals.append(logic.PropSymbolExpr(pacman_str, x, y + 1, t-1)&logic.PropSymbolExpr('South', t-1))
if not walls_grid[x][y - 1]:
literals.append(logic.PropSymbolExpr(pacman_str, x, y - 1, t-1)&logic.PropSymbolExpr('North', t-1))
if not walls_grid[x + 1][y]:
literals.append(logic.PropSymbolExpr(pacman_str, x + 1, y, t-1)&logic.PropSymbolExpr('West', t-1))
if not walls_grid[x - 1][y]:
literals.append(logic.PropSymbolExpr(pacman_str, x - 1, y, t-1)&logic.PropSymbolExpr('East', t-1))
expression = logic.PropSymbolExpr(pacman_str, x, y, t) % logic.disjoin(literals)
return logic.to_cnf(expression)
def pacmanAliveSuccessorStateAxioms(x, y, t, num_ghosts):
"""
Successor state axiom for patrolling ghost state (x,y,t) (from t-1).
Current <==> (causes to stay) | (causes of current)
"""
ghost_strs = [ghost_pos_str+str(ghost_num) for ghost_num in xrange(num_ghosts)]
alive = logic.PropSymbolExpr(pacman_alive_str, t)
lst = []
e = []
for g in ghost_strs:
e.append(~logic.PropSymbolExpr(g, x, y, t-1))
e.append(~logic.PropSymbolExpr(g, x, y, t))
q = logic.conjoin(e)
lst.append(q)
lst.append(~logic.PropSymbolExpr(pacman_str, x, y, t))
res = logic.disjoin(lst)
if len(lst) == 0:
return alive % alive
return alive % (logic.conjoin([logic.PropSymbolExpr(pacman_alive_str, t-1), res]))
def sentence1():
"""Returns a logic.Expr instance that encodes that the following expressions are all true.
A or B
(not A) if and only if ((not B) or C)
(not A) or (not B) or C
"""
"*** YOUR CODE HERE ***"
A = logic.Expr('A')
B = logic.Expr('B')
C = logic.Expr('C')
a_or_b = A | B
notA, notB = ~A, ~B
notB_or_C = notB | C
notA_iff = notA % notB_or_C
notA_or_else = logic.disjoin([notA,notB,C])
return logic.conjoin([(a_or_b),(notA_iff),(notA_or_else)])
util.raiseNotDefined()
def atLeastOne(literals) :
"""
Given a list of logic.Expr literals (i.e. in the form A or ~A), return a single
logic.Expr instance in CNF (conjunctive normal form) that represents the logic
that at least one of the literals in the list is true.
>>> A = logic.PropSymbolExpr('A');
>>> B = logic.PropSymbolExpr('B');
>>> symbols = [A, B]
>>> atleast1 = atLeastOne(symbols)
>>> model1 = {A:False, B:False}
>>> print logic.pl_true(atleast1,model1)
False
>>> model2 = {A:False, B:True}
>>> print logic.pl_true(atleast1,model2)
True
>>> model3 = {A:True, B:True}
>>> print logic.pl_true(atleast1,model2)
True
"""
return logic.disjoin(literals)
def pacmanAliveSuccessorStateAxioms(x, y, t, num_ghosts):
"""
Successor state axiom for patrolling ghost state (x,y,t) (from t-1).
Current <==> (causes to stay) | (causes of current)
"""
ghost_strs = [ghost_pos_str+str(ghost_num) for ghost_num in xrange(num_ghosts)]
"*** YOUR CODE HERE ***"
lst1, lst2 = [], []
for g in ghost_strs:
lst1.append(logic.PropSymbolExpr(g, x, y, t))
lst2.append(logic.PropSymbolExpr(g, x, y, t - 1))
if len(ghost_strs):
causes = (logic.PropSymbolExpr(pacman_str, x, y, t) & logic.disjoin(lst2)) | logic.conjoin((logic.PropSymbolExpr(pacman_str, x, y, t), ~logic.disjoin(lst2), logic.disjoin(lst1)))
else:
return ~logic.PropSymbolExpr(pacman_alive_str, t) % ~logic.PropSymbolExpr(pacman_alive_str, t - 1)
#print logic.PropSymbolExpr(pacman_alive_str, t) % logic.conjoin(logic.PropSymbolExpr(pacman_alive_str, t - 1), cause)
return ~logic.PropSymbolExpr(pacman_alive_str, t) % ((logic.PropSymbolExpr(pacman_alive_str, t - 1) & causes) | ~logic.PropSymbolExpr(pacman_alive_str, t - 1))
def ghostPositionSuccessorStateAxioms(x, y, t, ghost_num, walls_grid):
"""
Successor state axiom for patrolling ghost state (x,y,t) (from t-1).
Current <==> (causes to stay) | (causes of current)
GE is going east, ~GE is going west
"""
pos_str = ghost_pos_str+str(ghost_num)
east_str = ghost_east_str+str(ghost_num)
"*** YOUR CODE HERE ***"
lst = []
if not walls_grid[x - 1][y]:
lst.append(logic.PropSymbolExpr(pos_str, x - 1, y, t - 1) & logic.PropSymbolExpr(east_str, t - 1))
if not walls_grid[x + 1][y]:
lst.append(logic.PropSymbolExpr(pos_str, x + 1, y, t - 1) & ~logic.PropSymbolExpr(east_str, t - 1))
if lst:
return logic.PropSymbolExpr(pos_str, x, y, t) % logic.disjoin(lst)
else:
return logic.PropSymbolExpr(pos_str, x, y, t) % logic.PropSymbolExpr(pos_str, x, y, t - 1)
def ghostDirectionSuccessorStateAxioms(t, ghost_num, blocked_west_positions, blocked_east_positions):
"""
Successor state axiom for patrolling ghost direction state (t) (from t-1).
west or east walls.
Current <==> (causes to stay) | (causes of current)
"""
pos_str = ghost_pos_str+str(ghost_num)
east_str = ghost_east_str+str(ghost_num)
"*** YOUR CODE HERE ***"
wlst, elst = [], []
for (x, y) in blocked_east_positions:
elst.append(~logic.PropSymbolExpr(pos_str, x, y, t))
for (x, y) in blocked_west_positions:
wlst.append(logic.PropSymbolExpr(pos_str, x, y, t))
if not elst and wlst:
return logic.PropSymbolExpr(east_str, t) % (logic.PropSymbolExpr(east_str, t - 1) | (~logic.PropSymbolExpr(east_str, t - 1) & logic.disjoin(wlst)))
elif elst and not wlst:
return logic.PropSymbolExpr(east_str, t) % (logic.PropSymbolExpr(east_str, t - 1) & logic.conjoin(elst))
elif not elst and not wlst:
return logic.PropSymbolExpr(east_str, t) % logic.PropSymbolExpr(east_str, t - 1)
else:
return logic.PropSymbolExpr(east_str, t) % ((logic.PropSymbolExpr(east_str, t - 1) & logic.conjoin(elst)) | (~logic.PropSymbolExpr(east_str, t - 1) & logic.disjoin(wlst)))
def atMostOne(literals):
"""
Given a list of Expr literals, return a single Expr instance in
CNF (conjunctive normal form) that represents the logic that at most one of
the expressions in the list is true.
"""
"*** BEGIN YOUR CODE HERE ***"
comb = list(itertools.combinations(literals, 2))
conj = disjoin(~comb[0][0], ~comb[0][1])
for i in comb[1:]:
conj = conjoin(conj, disjoin(~i[0], ~i[1]))
return conj
"*** END YOUR CODE HERE ***"