Due: Friday 2/25 at 10:59 pm
In this project, you will use/write simple Python functions that generate logical sentences describing Pacman physics, aka pacphysics. Then you will use a SAT solver, pycosat, to solve the logical inference tasks associated with planning (generating action sequences to reach goal locations and eat all the dots), localization (finding oneself in a map, given a local sensor model), mapping (building the map from scratch), and SLAM (simultaneous localization and mapping).
As in previous programming assignments, this assignment includes an autograder for you to grade your answers on your machine. This can be run with the command:
python autograder.py
See the autograder tutorial in Project 0 for more information about using the autograder.
The code for this project consists of several Python files, some of which you will need to read and understand in order to complete the assignment, and some of which you can ignore. You can download all the code and supporting files as a zip archive.
logicPlan.py |
Where you will put your code for the various logical agents. |
logic.py |
Propsitional logic code originally from https://code.google.com/p/aima-python/ with modifications for our project. There are several useful utility functions for working with logic in here. |
logicAgents.py |
The file that defines in logical planning form the two specific problems that Pacman will encounter in this project. |
pycosat_test.py |
Quick test main function that checks that the pycosat module is installed correctly. |
game.py |
The internal simulator code for the Pacman world. The only thing you might want to look at in here is the Grid class. |
test_cases/ |
Directory containing the test cases for each question |
pacman.py |
The main file that runs Pacman games. |
logic_util.py |
Utility functions for logic.py |
util.py |
Utility functions primarily for other projects. |
logic_planTestClasses.py |
Project specific autograding test classes |
graphicsDisplay.py |
Graphics for Pacman |
graphicsUtils.py |
Support for Pacman graphics |
textDisplay.py |
ASCII graphics for Pacman |
ghostAgents.py |
Agents to control ghosts |
keyboardAgents.py |
Keyboard interfaces to control Pacman |
layout.py |
Code for reading layout files and storing their contents |
autograder.py |
Project autograder |
testParser.py |
Parses autograder test and solution files |
testClasses.py |
General autograding test classes |
Files to Edit and Submit: You will fill in portions of logicPlan.py
during the assignment. You should submit these files with your code and comments. Please do not change the other files in this distribution or submit any of our original files other than these files.
Evaluation: Your code will be autograded for technical correctness. Please do not change the names of any provided functions or classes within the code, or you will wreak havoc on the autograder. However, the correctness of your implementation -- not the autograder's judgements -- will be the final judge of your score. If necessary, we will review and grade assignments individually to ensure that you receive due credit for your work.
Academic Dishonesty: We will be checking your code against other submissions in the class for logical redundancy. If you copy someone else's code and submit it with minor changes, we will know. These cheat detectors are quite hard to fool, so please don't try. We trust you all to submit your own work only; please don't let us down. If you do, we will pursue the strongest consequences available to us.
Getting Help: You are not alone! If you find yourself stuck on something, contact the course staff for help. Office hours, section, and the discussion forum are there for your support; please use them. If you can't make our office hours, let us know and we will schedule more. We want these projects to be rewarding and instructional, not frustrating and demoralizing. But, we don't know when or how to help unless you ask.
Discussion: Please be careful not to post spoilers.
In the first part of this project, you will be working with the Expr
class defined in logic.py
to build propositional logic sentences. An Expr
object is implemented as a tree with logical operators (∧, ∨, ¬, →, ↔) at each node and with literals (A, B, C) at the leaves. Here is an example sentence and its representation:
(A ∧ B) ↔ (¬ C ∨ D)
To instantiate a symbol named 'A', call the constructor like this:
A = Expr('A')
The Expr
class allows you to use Python operators to build up these expressions. The following are the available Python operators and their meanings:
~A
: ¬ AA & B
: A ∧ BA | B
: A ∨ BA >> B
: A → BA % B
: A ↔ BSo to build the expression A ∧ B, you would type this:
A = Expr('A')
B = Expr('B')
a_and_b = A & B
(Note that A
to the left of the assignment operator in that example is just a Python variable name, i.e. symbol1 = Expr('A')
would have worked just as well.)
conjoin
and disjoin
One last important thing to note is that conjoin
and disjoin
operators wherever possible. conjoin
creates a chained &
(logical AND) expression, and disjoin
creates a chained |
(logical OR) expression. Let's say you wanted to check whether conditions A, B, C, D, and E are all true. The naive way to achieve this is writing condition = A & B & C & D & E
, but this actually translates to ((((A & B) & C) & D) & E)
, which creates a very nested logic tree (see (1)
in diagram below) and becomes a nightmare to debug. Instead, conjoin
makes a flat tree (see (2)
in diagram below).
For the rest of the project, please use the following variable naming conventions:
Expr
).A-Z
, a-z
, 0-9
, _
, ^
, [
, ]
.&
, |
) must not appear in variable names. So, Expr('A & B')
is illegal because it attempts to create a single constant symbol named 'A & B'
. We would use Expr('A') & Expr('B')
to make a logical expression.PropSymbolExpr(pacman_str, x, y, time=t)
: whether or not Pacman is at (x, y) at time t, writes P[x,y]_t
.PropSymbolExpr(wall_str, x, y)
: whether or not a wall is at (x, y), writes WALL[x,y]
.PropSymbolExpr(action, time=t)
: whether or not pacman takes action action
at time t, where action
is an element of DIRECTIONS
, writes i.e. North_t
.PropSymbolExpr(str, a1, a2, a3, a4, time=a5)
creates the expression str[a1,a2,a3,a4]_a5
where str
is just a string.There is additional, more detailed documentation for the Expr
class in logic.py
.
A SAT (satisfiability) solver takes a logic expression which encodes the rules of the world and returns a model (true and false assignments to logic symbols) that satisfies that expression if such a model exists. To efficiently find a possible model from an expression, we take advantage of the pycosat module, which is a Python wrapper around the picoSAT library.
Unfortunately, this requires installing this module/library on each machine.
To install this software on your conda env, please follow these steps:
conda activate cs188
(if your env is called cs188
)
pip install pycosat
. (Note: you may need to run: sudo pip3 install pycosat
.) If you get errors, try instead conda install -c anaconda pycosat
.Testing pycosat installation:
After unzipping the project code and changing to the project code directory, run:
python pycosat_test.py
This should output:
[1, -2, -3, -4, 5].
Please let us know if you have issues with this setup. This is critical to completing the project, and we don't want you to spend your time fighting with this installation process.
This question will give you practice working with the Expr
data type used in the project to represent propositional logic sentences. You will implement the following functions in logicPlan.py
:
sentence1()
: Create one Expr
instance that represents the proposition that the following three sentences are true. Do not do any logical simplification, just put them in a list in this order, and return the list conjoined. Each element of your list should correspond to each of the three sentences.A ∨ B
¬ A ↔ (¬ B ∨ C)
¬ A ∨ ¬ B ∨ C
sentence2()
: Create one Expr
instance that represents the proposition that the following four sentences are true. Again, do not do any logical simplification, just put them in a list in this order, and return the list conjoined.C ↔ (B ∨ D)
A → (¬ B ∧ ¬ D)
¬ (B ∧ ¬ C) → A
¬ D → C
sentence3()
: Using the PropSymbolExpr
constructor, create symbols named PacmanAlive_0
, PacmanAlive_1
, PacmanBorn_0
, and PacmanKilled_0
. Hint: recall that PropSymbolExpr(str,
a1, a2, a3, a4, time=a5)
creates the expression str[a1,a2,a3,a4]_a5
where str
is a string; you should make some strings for this problem. Then, create one Expr
instance which encodes the following three English sentences as propositional logic in this order without any simplification:findModelCheck()
:findModel(sentence)
method works: it uses to_cnf
to convert the input sentence into Conjunctive Normal Form (the form required by the SAT solver), and passes it to the SAT solver to find a satisfying assignment to the symbols in sentence
, i.e., a model. A model is a dictionary of the symbols in your expression and a corresponding assignment of True or False. Test your sentence1()
, sentence2()
, and sentence3()
with findModel
by opening an interactive session in Python and running from logicPlan import *
and findModel(sentence1())
and similar queries for the other two. Do they match what you thought?findModelCheck
so that it returns something that looks the exact same as findModel(Expr('a'))
in a Python interactive session would if lower-cased letters were allowed. You should not use
findModel
or Expr
, simply directly recreate the output. For instance, if the output was [(MyVariable, True)]
, something close to the solution would be return [("MyVariable", True)]
.entails(premise, conclusion)
: Return True if and only if the premise
entails the conclusion
. Hint: findModel
is helpful here; think about what must be unsatisfiable in order for the entails to be True, and what it means for something to be unstatisfiable.plTrueInverse(assignments, inverse_statement)
: Returns True if and only if the (not inverse_statement) is True given assignments.Before you continue, try instantiating a small sentence, e.g. A ∧ B → C, and call to_cnf
on it. Inspect the output and make sure you understand it (refer to AIMA section 7.5.2 for details on the algorithm to_cnf
implements).
To test and debug your code run:
python autograder.py -q q1
Implement the following three functions in logicPlan.py
:
atLeastOne(literals)
: Return a single expression (Expr) in CNF that is true only if at least one expression in the input list is true. Each input expression will be a literal.atMostOne(literals)
: Return a single expression (Expr) in CNF that is true only if at most one expression in the input list is true. Each input expression will be a literal. HINT: Use itertools.combinations
. If you have `n` literals, and at most one is true, your resulting CNF expression should be a conjunction of $n \choose 2$ clauses.exactlyOne(literals)
: Return a single expression (Expr) in CNF that is true only if exactly one expression in the input list is true. Each input expression will be a literal. If you decide to call your previously implemented atLeastOne
and atMostOne
, call atLeastOne
first to pass our autograder for q3.Each of these methods takes a list of Expr
literals and returns a single Expr
expression that represents the appropriate logical relationship between the expressions in the input list. An additional requirement is that the returned Expr must be in CNF (conjunctive normal form). You may NOT use the to_cnf
function in your method implementations (or any of the helper functions logic.eliminate_implications
, logic.move_not_inwards
, and logic.distribute_and_over_or
).
Don't run to_cnf on your knowledge base when implementing your planning agents in later questions. This is because to_cnf
makes your logical expression much longer sometimes, so you want to minimize this effect, and findModel does this already. In later questions, reuse your implementations for atLeastOne(.)
, atMostOne(.)
, and exactlyOne(.)
instead of re-engineering these functions (to avoid accidentally making an unreasonably slow non-CNF-based implementation) from scratch.
You may utilize the logic.pl_true
function to test the output of your expressions. pl_true
takes an expression and a model and returns True if and only if the expression is true given the model.
To test and debug your code run:
python autograder.py -q q2
In this question, you will implement the basic pacphysics logical expressions, as well as learn how to prove where pacman is and isn’t by building an appropriate knowledge base (KB) of logical expressions.
Implement the following functions in logicPlan.py
:
pacmanSuccessorAxiomSingle
: This generates an expression defining the sufficient and necessary conditions for Pacman to be at (x, y) at t:Expr
. Make sure to use disjoin
and conjoin
where appropriate. Looking at SLAMSuccessorAxiomSingle
may be helpful, although note that the rules there are more complicated than in this function. The simpler side of the biconditional should be on the left for autograder purposes.pacphysicsAxioms
: Here, you will generate a bunch of physics axioms. For timestep t:t
= time, all_coords
and non_outer_wall_coords
are lists of (x, y) tuples.walls_grid
is only passed through to successorAxioms
and describes (known) walls.sensorModel(t: int, non_outer_wall_coords) -> Expr
returns a single Expr
describing observation rules; you can take a look at sensorAxioms
and SLAMSensorAxioms
to see examples of this.successorAxioms(t: int, walls_grid, non_outer_wall_coords) -> Expr
describes transition rules, e.g. how previous locations and actions of Pacman affect the current location; we have seen this in the functions in the previous bullet point.all_coords
, append the following implication (if-then form): if a wall is at (x, y), then Pacman is not at (x, y) at t.non_outer_wall_coords
at timestep t.DIRECTIONS
at timestep t.sensorAxioms
. All callers except for checkLocationSatisfiability
make use of this; how to handle the case where we don't want any sensor axioms added is up to you.successorAxioms
. All callers will use this.pacphysics_sentences
. As you can see in the return statement, these will be conjoined and returned.def myFunction(x, y, t): return PropSymbolExpr('hello', x, y, time=t)
be a function we want to use.def myCaller(func: Callable): ...
be the caller that wants to use a function.myCaller(myFunction)
(note that myFunction
is not called with ()
after it).myFunction
by having inside myCaller
this: useful_return = func(0, 1, q)
.checkLocationSatisfiability
: Given a transition (x0_y0, action0, x1_y1
), action1
, and a problem
, you will write a function that will return a tuple of two models (model1, model2)
.
model1
, Pacman is at (x1, y1) at time t = 1 given x0_y0, action0, action1
, proving that it's possible that Pacman there. Notably, if model1
is False
, we know Pacman is guaranteed to NOT be there.model2
, Pacman is NOT at (x1, y1) at time t = 1 given x0_y0, action0, action1
, proving that it's possible that Pacman is not there. Notably, if model2
is False
, we know Pacman is guaranteed to be there.action1
has no effect on determining whether the Pacman is at the location; it's there just to match your solution to the autograder solution.pacphysics_axioms(...)
with the appropriate timesteps. There is no sensorModel
because we know everything about the world. Where needed, use allLegalSuccessorAxioms
for transitions since this is for regular Pacman transition rules.action0
action1
findModel
for two models described earlier. The queries should be different; for a reminder on how to make queries see entails
.Reminder: the variable for whether Pacman is at (x, y) at time t is PropSymbolExpr(pacman_str, x, y, time=t)
, wall exists at (x, y) is PropSymbolExpr(wall_str, x, y)
, and action is taken at t is PropSymbolExpr(action, time=t)
.
To test and debug your code run:
python autograder.py -q q3
Pacman is trying to find the end of the maze (the goal position). Implement the following method using propositional logic to plan Pacman's sequence of actions leading him to the goal:
Disclaimer: the methods from now on will be decently slow. This is because a SAT solver is very general and simply crunches logic, unlike our previous algorithms that employ a specific human-created algorithm to specific type of problem. Of note, Pycosat's main algorithm is in C, which is generally a much much faster language to execute than Python, and it's still this slow.
positionLogicPlan(problem)
: Given an instance of logicPlan.PlanningProblem
, returns a sequence of action strings for the Pacman agent to execute.You will not be implementing a search algorithm, but creating expressions that represent pacphysics for all possible positions at each time step. This means that at each time step, you should be adding general rules for all possible locations on the grid, where the rules do not assume anything about Pacman's current position.
You will need to code up the following sentences for your knowledge base, in the following pseudocode form:
exactlyOne
of the locations in non_wall_coords
at timestep t. This is similar to pacphysicsAxioms
, but don't use that method since we are using non_wall_coors
when generating the list of possible locations in the first place (and walls_grid
later).findModel
and pass in the Goal Assertion and KB
.extractActionSequence
.pacmanSuccessorAxiomSingle(...)
for all possible pacman positions in non_wall_coords
.Test your code on smaller mazes using:
python pacman.py -l maze2x2 -p LogicAgent -a fn=plp
python pacman.py -l tinyMaze -p LogicAgent -a fn=plp
To test and debug your code run:
python autograder.py -q q4
Note that with the way we have Pacman's grid laid out, the leftmost, bottommost space occupiable by Pacman (assuming there isn't a wall there) is (1, 1), as shown below (not (0, 0)).
Summary of Pacphysics used in Q3 and Q4 (also found at AIMA chapter 7.7):
Note that the above always hold true regardless of any specific game, actions, etc. To the above always-true/ axiom rules, we add information consistent with what we know.
Debugging hints:
(1, 1)
at time 0 and at (4, 4)
at time 6, he was never at (5, 5)
at any time in between.exactlyOne
and atMostOne
, and ensure that you're using as few clauses as possible.Pacman is trying to eat all of the food on the board. Implement the following method using propositional logic to plan Pacman's sequence of actions leading him to the goal.
foodLogicPlan(problem)
: Given an instance of logicPlan.PlanningProblem
, returns a sequence of action strings for the Pacman agent to execute.This question has the same general format as question 4; you may copy your code from there as a starting point. The notes and hints from question 4 apply to this question as well. You are responsible for implementing whichever successor state axioms are necessary that were not implemented in previous questions.
What you will change from the previous question:
PropSymbolExpr(food_str, x, y, time=t)
, where each variable is true if and only if there is a food at (x, y) at time t.Test your code using:
python pacman.py -l testSearch -p LogicAgent -a fn=flp,prob=FoodPlanningProblem
We will not test your code on any layouts that require more than 50 time steps.
To test and debug your code run:
python autograder.py -q q5
For the remaining questions, we will rely on the following helper functions, which will be referenced by the pseudocode for localization, mapping, and SLAM.
pacphysics_axioms(...)
, which you wrote in q3. Use sensorAxioms
and allLegalSuccessorAxioms
for localization and mapping, and SLAMSensorAxioms
and SLAMSuccessorAxioms
for SLAM only.agent.actions[t]
agent.getPercepts()
and pass the percepts to fourBitPerceptRules(...)
for localization and mapping, or numAdjWallsPerceptRules(...)
for SLAM. Add the resulting percept_rules to KB
.possible_locations = []
non_outer_wall_coords
.entails
and the KB
.possible_locations
.non_outer_wall_coords
.entails
and the KB
.known_map
: (x, y) locations where there is provably a wall.known_map
: (x, y) locations where there is provably not a wall.Observation: we add known Pacman locations and walls to KB so that we don't have to redo the work of finding this on later timesteps; this is technically redundant information since we proved it using the KB in the first place.
Pacman starts with a known map, but unknown starting location. It has a 4-bit sensor that returns whether there is a wall in its NSEW directions. (For example, 1001 means there is a wall to pacman's North and West directions, and these 4-bits are represented using a list with 4 booleans.) By keeping track of these sensor readings and the action it took at each timestep, Pacman is able to pinpoint its location. You will code up the sentences that help Pacman determine the possible locations it can be at each timestep by implementing:
localization(problem, agent)
: Given an instance of logicPlan.LocalizationProblem
and an instance of logicAgents.LocalizationLogicAgent
, repeatedly yields for timesteps t between 0 and agent.num_steps-1
a list of possible locations (x_i, y_i) at t: [(x_0_0, y_0_0), (x_1_0, y_1_0), ...]. Note that you don't need to worry about how generators work as that line is already written for you.For Pacman to make use of sensor information during localization, you will use two methods already implemented for you: sensorAxioms
-- i.e. Blocked[Direction]_t ↔ [(P[x_i, y_j]_t ∧ WALL[x_i+dx, y_j+dy]) ∨ (P[x_i', y_j']_t ∧ WALL[x_i'+dx, y_j'+dy]) ... ] -- and fourBitPerceptRules
, which translate the percepts at time t into logic sentences.
Please implement the function according to our pseudocode:
KB
: where the walls are (walls_list
) and aren't (not in walls_list
).range(agent.num_timesteps)
:agent.moveToNextState(action_t)
on the current agent action at timestep t.yield
the possible locations.Note on display: the yellow Pacman is where he is at the time that's currently being calculated, so possible locations and known walls and free spaces are from the previous timestep.
To test and debug your code run:
python autograder.py -q q6
Pacman now knows his starting location, but does not know where the walls are (other than the fact that the border of outer coordinates are walls). Similar to localization, it has a 4-bit sensor that returns whether there is a wall in its NSEW directions. You will code up the sentences that help Pacman determine the location of the walls by implementing:
mapping(problem, agent)
: Given an instance of logicPlan.MappingProblem
and an instance of logicAgents.MappingLogicAgent
, repeatedly yields for timesteps t between 0 and agent.num_steps-1
knowledge about the map [[1, 1, 1, 1], [1, -1, 0, 0], ... ] at t. Note that you don't need to worry about how generators work as that line is already written for you.
known_map
:known_map
is a 2D-array (list of lists) of size (problem.getWidth()+2, problem.getHeight()+2), because we have walls around the problem.known_map
is 1 if (x, y) is guaranteed to be a wall at timestep t, 0 if (x, y) is guaranteed to not be a wall, and -1 if (x, y) is still ambiguous at timestep t.Please implement the function according to our pseudocode:
(pac_x_0, pac_y_0)
of Pacman, and add this to KB
. Also add whether there is a wall at that location.range(agent.num_timesteps)
:agent.moveToNextState(action_t)
on the current agent action at timestep t.yield known_map
To test and debug your code run:
python autograder.py -q q7
Sometimes Pacman is just really lost and in the dark at the same time. In SLAM (Simultaneous Localization and Mapping), Pacman knows his initial coordinates, but does not know where the walls are. In SLAM, Pacman may inadvertently take illegal actions (for example, going North when there is a wall blocking that action), which will add to the uncertainty of Pacman's location over time. Additionally, in our setup of SLAM, Pacman no longer has a 4 bit sensor that tells us whether there is a wall in the four directions, but only has a 3-bit sensor that reveals the number of walls he is adjacent to. (This is sort of like wifi signal-strength bars; 000 = not adjacent to any wall; 100 = adjacent to exactly 1 wall; 110 = adjacent to exactly 2 walls; 111 = adjacent to exactly 3 walls. These 3 bits are represented by a list of 3 booleans.) Thus, instead of using sensorAxioms
and fourBitPerceptRules
, you will use SLAMSensorAxioms
and numAdjWallsPerceptRules
. You will code up the sentences that help Pacman determine (1) his possible locations at each timestep, and (2) the location of the walls, by implementing:
slam(problem, agent)
: Given an instance of logicPlan.SLAMProblem
and logicAgents.SLAMLogicAgent
, repeatedly yields a tuple of two items:
known_map
at t (of the same format as in question 6 (mapping))To pass the autograder, please implement the function according to our pseudocode:
(pac_x_0, pac_y_0)
of Pacman, and add this to KB
. Update known_map
accordingly and add the appropriate expression to KB.range(agent.num_timesteps)
:SLAMSensorAxioms
, SLAMSuccessorAxioms
, and numAdjWallsPerceptRules
.agent.moveToNextState(action_t)
on the current agent action at timestep t.yield known_map, possible_locations
To test and debug your code run (note: this is slow, staff solution takes 3.5 minutes to run to completion on a good laptop processor):
python autograder.py -q q8
In order to submit your project, run python submission_autograder.py
and submit the generated token file logic.token
to the Project 3
assignment on Gradescope.