Assignment 3

Written Assignment - Predicate Logic & Planning

Task 1 (CSE 4308: 15 Points; CSE 5360: 15 points)

Consider a knowledge base with these facts:

There is a dog called Shadow.
John gave Shadow to Mary.
If Shadow is male, Mary gave a smartphone to John.
If Shadow is female, Mary gave John a laptop.
John only gives male dogs to people (Interpret it as if John gives dogs to people they are male).
Mary gave John a laptop.

Convert the above knowledge-base to a first-order logic knowledge base. For each predicate, function, constant, or variable that you use, explicitly state:

What type of entity it is (is it a predicate, function, constant, or variable).
What its semantics are (what it means).

Task 2 (CSE 4308: 5 Points; CSE 5360: 5 points)

Try and unifiy the following predicates(if possible)

taller(John, y), taller(x, Son(x))

taller(y, Barry), taller(Barry, x)

taller(x, Jane), taller(Bob, Jane)

taller(Son(x), Jane), taller(Bob, Jane)

taller(Barry, John), taller(x, y)

Task 3 (CSE 4308: 10 Points; CSE 5360: 10 points)

List all the symbols required to convert the given KB to Propositional Logic. Your symbols should be comprehensive enough that any statement using the predicates and constants used in the KB below can be converted. Also convert the given KB

Faster(Sam, John)
for-all x,y: Taller(x,y) <=> Faster(y,x)

Show the the following KB entails

Taller(John,Sam)

by propositionalization

Task 4 (CSE 4308: 30 Points; CSE 5360: 30 points)

The task in this programming assignment is to design appropriate descriptions of facts, actions, and goals, using the PDDL language, for the Tower of Hanoi problem. You will use your descriptions as inputs to a Graphplan implementation. If your descriptions are correct, Graphplan will produce appropriate plans.

Compiling and Running the Software

The Graphplan software can be downloaded from graphplan.zip. See the README file in that package for additional information. To compile the software on omega, unzip the directory, and, from that directory, type

make graphplan

Once the program compiles, it can be invoked from the commandline as follows:

graphplan -o [operators_file] -f [facts_file]

For example:

graphplan -o block_ops.txt -f block_facts3.txt

Argument operators_file specifies the location of a text file containing definitions of actions. For example, see block_ops.txt for definitions of actions appropriate for the blocks world domain.
Argument facts_file specifies the location of a text file containing definitions of facts about the environment, including objects (and types for those objects), general predicates that are always true, initial state description, and goal description. For example, see block_facts2.txt, block_facts3.txt, and block_facts4.txt for example fact descriptions for the blocks world domain.

Once you start running the software, it will ask you three questions. Just hit enter for each question, so as to use the default settings. If your descriptions of actions and facts are correct, the program will print out a plan achieving the stated goal.

Note that the preconds in each fact file will contain both statements that are always true in that domain (i.e., in the Tower of Hanoi domain or the blocks world domain), and statements that simply describe the initial state for that specific planning problem. In addition to the facts files for the specific planning problems you are given, you will have to create a separate text file that includes all the statements that must be present in ANY facts file for that domain.

Tower of Hanoi Description

A description of the Tower of Hanoi domain can be found at Wikipedia. In all problems that your program will be tested with there will be five discs (called disk1, disk2, disk3, disk4, disk5) and three pegs (called A, B, C). In all your facts files you will have to include both a common part (defining objects and relations among objects) and a plan-specific part (describing the initial state and goal for each plan). Note that some of the five disks may not appear in some of the planning problems.

The two planning problems you have to solve are:

Problem 1

initial state:
(on disk1 disk2)
(on disk2 A) 
(clear disk1)
(clear B)
(clear C) 

goal:
(on disk1 B)
(on disk2 C)

Problem 2

initial state:
(on disk1 disk2) 
(on disk2 disk3)
(on disk3 disk4)
(on disk4 disk5)
(on disk5 C) 
(clear disk1) 
(clear A) 
(clear B)

goal:
(on disk1 disk2) 
(on disk2 disk3)
(on disk3 disk4)
(on disk4 disk5)
(on disk5 A)

Grading

This task will be graded for 30 points. Specifically, the point allocation is:

15 points: defining facts and actions correctly. The language that you define (i.e., the actions, objects, and general statements that are always true) should be sufficient not only for the specific plans that you are required to construct, but also for any other planning problems that we can define in the Tower of Hanoi domain. As part of grading, we will also test your solutions on planning problems that we will make up.
15 points: solving the planning problems you are given + 1 additional problem per domain. You get 5 points for each problem. If you solve all 3 correctly, you get 15 points.

Task 5 (CSE 4308: 25 Points; CSE 5360: 20 points)

Three adults and three children are on the left side of the river. Each adult weighs 150 pounds. Each child has half the weight of an adult, so each child weighs 75 pounds. They all want to cross to the right side of the river. However, the only means of transportation they can use is a boat, and the boat can carry a maximum of 150 pounds. Thus, the boat can carry one adult without children, or one child, or two children. Any adult or child can operate the boat, but the boat cannot be operated without having at least one person on the boat. The goal is to come up with a plan for moving everyone from the left side to the right side using multiple boat trips.

Describe the initial state and the goal, using PDDL. Define appropriate actions for this planning problem, in the PDDL language. For each action, provide a name, arguments, preconditions, and effects. Also, give a complete plan (using the actions described) for getting from the start to the goal state

Task 6 (CSE 4308: 15 Points; CSE 5360: 10 points)

Suppose that we are using PDDL to describe facts and actions in a certain world called JUNGLE. In the JUNGLE world there are 5 predicates, each predicate takes at most 3 arguments, and there are 4 constants. Give a reasonably tight bound on the number of unique states in the JUNGLE world. Justify your answer.

Task 7 (CSE 4308: 10 Points (EC); CSE 5360: 10 points)

Consider the problem in Task 5. Let us say that, if there is only one person in the boat, the boat can be blown off course and end up back on the side it originally started from. How would you modify the actions you described in Task 2 to account for this if you were going to try and handle this scenario by

Execution Monitoring/Online Replanning
Conditional Planning

In both cases, show what the modifications are (If no modification is necessary, Justify).