CAP4630 Homework 4 (14 pts)
Due April 13
Question 1: Please show detailed steps that sentence )( 4,23,14,1 PPB ∨
⇔
can be
decomposed into CNF (1 pts)
Question 2: Minesweeper, the well-known computer game, is closely related to the
wumpus world. A minesweeper world is a rectangular grid of N squares with M invisible
mines scattered among them. Any square may be probed by the agent; instance death
follows if a mine is probed. Minesweeper indicates the presence of mines by revealing, in
each probed square, the number of mines that are directly or diagonally adjacent. The
goal is to have probed every unmined square.
a. Let Xi,j be true iff square [i,j] contains a mine. Write down the assertion that there
are exactly two mines adjacent to [1,1] as a sentence involving some logical
combination of Xi,j propositions (1 pt)
b. Generalize your assertion from (a) by explaining how to construct a CNF
sentence asserting that k of n neighbors contain mines (1pt)
Question 3: What is a Horn Clause? (0.5 pt) What is the purpose of using horn clauses?
(0.5 pt). Given the following knowledge base of Horn clauses, please draw the
corresponding AND-OR graph (1 pt). Please using PL-FC-ENTAIL?(KB, q) to whether
KB╞Q is true or not (show your solutions 2 pts)
P⇒Q; B∧L∧M⇒ P; A∧L⇒M; A∧B⇒L; A; B;
Question 4: What is a decision tree (0.25 pt), what is entropy (0.25), what is information
gain (0.25 pt), what is information gain ratio (0.25 pt), what is the bias of the decision
tree (0.25 pt), what is the bias of the information gain (0.25 pt), what is overfitting in
decision tree construction (0.25 pt), how to avoid overfitting (0.25 pt).
