assignment

Assignments:

Assignment 1: The Zebra Problem

Last Date for Submission:
(Please mail the submission to the TA)

Consider the following logic puzzle: In five houses, each with a different color, live 5 persons of different nationalities, each of whom prefer a different brand of cigarette, a different drink, and a different pet. Given the following facts, the question to answer is "Where does the Zebra live, and in which house do the people drink water?"

The Englishman lives in the red house.
The Spaniard owns a dog.
The Norweigian lives in the first house on the left.
Kools (a cigarette brand) are smoked in the yellow house.
The man who smokes Chesterfields lives in the house next to the man with the fox.
The Norweigean lives next to the blue house.
The Winston smoker owns snails.
The Luck Strike smoker drinks orange juice.
The Ukranian drinks tea.
The Japanese smokes Parliaments.
Kools are smoked in the house next to the house where the horses are kept.
Coffee is drunk in the green house.
The green house is immediately to the right (your right) of the ivory house.
Milk is drunk in the middle house.

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1. Discuss different representations of this problem as a CSP.
2. Choose the best representation (you feel).
3. Write a program to solve the CSP (and thus answer the above questions) with the chosen representation.

Assignment 2: Knowledge Based Systems and Reasoning

Last Date for Submission:
(Please mail or manually submit the soft/hard/handwritten solution to the TA)

Part A: Inferencing in FOL
From the statement "Horses are animals." it follows that "The head of a horse is the head of an animal." Demonstrate that this inference is valid by carrying out the following steps:

i. Translate the premise and the claculation into the language of first-order logic. Use three predicates: HeadOf(h,x) (meaning "h is a head of x"), Horse(x), and Animal(x).
ii. Negate the conclusion, and convert the premise and the negated conclusion into conjunctive normal form.
iii. Use resolution to show that the conclusion follows from the premise.

Part B: Knowledge Representation

Road Network around Kharagpur (not to scale)

Consider the above road network. Vertices represent towns and edges represent roads. Edge weights represent distances. Consider the problem of planning a route for a robot from one town to another. The basic action taken by the robot is Go(x,y) , which takes it from town x to town y if there is a direct route (one hop) between those towns. DirectRoute(x,y) is true if and only if there is a direct route from x to y. Assume that all these facts have already been extracted from the map and included in the KB. The robot begins in Bokaro and must reach Kharagpur.

i. Write a suitable logical description of the initial situation of the robot.
ii. Write a suitable logical query whose solution will provide possible paths to the goal.
iii. Write a statement describing the Go action.
iv. Now suppose that travelling through a direct route between two towns consumes an amount of fuel equal to the distance between the towns. The robot starts with fuel at full capacity. Augment your representation to include these considerations. Your action dscription should be such that the query you specified earlier will still result in feasible plans.
v. Describe the initial situation with these new considerations, and write new rules to describe the Go action.
vi. Now suppose that some of the vertices are also fuel stations, at which the robot can fill its tank. Extend your representation and write all the rules necessary to represent fuel stations, including the Fillup action.

Assignment 3: Bayesian Networks

Last Date for Submission:
(Please mail or manually submit the soft/hard/handwritten solution to the TA)

(Part I) In a nuclear power plant, there is an alarm that senses when a temperature gauge exceeds a given threshold. The gauge measures the core temperature. Consider the Boolean variables A (alarm sounds), FA (alarm is faulty), and FG (gauge is faulty), and the multivalued nodes G (gauge reading) and T (actual core temperature).

a. Draw a plausible belief net for this domain, given that the gauge is more likely to fail when the core temperature gets too high.
b. Is the network a polytree?
c. Suppose there are just two possible actual and measured temperatures, Normal and High, and that the gauge gives the incorrect temperature x% of the time when it is working, but y% of the time when it is faulty. Give the conditional probability table associated with G.
d. Suppose the alarm works unless it is faulty, in which case it never goes off. Give the conditional probability table associated with A.
e. Suppose the alarm and gauge are working, and the alarm sounds. Calculate the probability that the core temperature is too high.

(Part II) In the network below, list all pairs of independent variables and all pairs of conditionally independent variables (and their associated conditioned variable).