CS 188 Introduction to AI
Fall 2002 Stuart Russell Final Solutions
1. (10 pts.) Some Easy Questions to Start With
(a) (2) False; ambiguity resolution often requires commonsense knowledge, context, etc. Dictionaries often
giv multiple definitions of a word, which is one source of ambiguity.
(b) (2) True; it’s hard to see directly into the mental state of other humans.
(c) (2) False; feedforward NNs have no internal state, hence cannot track a partially observable environment.
(d) (2) False; obviously it depends on how well it’s programmed, and we don’t know how to do that yet
(despite what Kurzweil, Moravec, Joy, and others suggest).
(e) (2) False; odometry errors accumulate over time; the robot must sense its environment.
2. (13 pts.) Search
(a) (1) The branching factor is 4 (number of neighbors of each location).
(b) (2) The states at depth kform a square rotated at 45 degrees to the grid. Obviously there are a linear
number of states along the boundary of the square, so the answer is 4k.
(c) (2) Without repeated state checking, BFS expends exponentially many nodes: counting precisely, we get
((4x+y+1 −1)/3) −1.
(d) (2) There are quadratically many states within the square for depth x+y, so the answer is 2(x+y)(x+
y+ 1) −1.
(e) (2) True; this is the Manhattan distance metric.
(f) (2) False; all nodes in the rectangle defined by (0,0) and (x, y) are candidates for the optimal path, and
there are quadratically many of them, all of which may be expended in the worst case.
(g) (1) True; removing links may induce detours, which require more steps, so his an underestimate.
(h) (1) False; nonlocal links can reduce the actual path length below the Manhattan distance.
3. (6 pts.) Propositional Logic
(a) (1) False; {A=false, B =f alse}satisfies A⇔Bbut not A∨B.
(b) (1) True; ¬A∨Bis the same as A⇒B, which is entailed by A⇔B.
(c) (2) True; the first conjunct has models and entails the second.
(d) (2) True; both have four models in A,B,C.
4. (10 pts.) First-Order Logic
(a) (3) “Every cat loves its mother or father” can be translated as
i. ∀x¬Cat(x)∨Loves(x, M other(x)) ∨Loves(x, F ather(x)).
(b) (3) “Every dog who loves one of its brothers is happy” can be translated as
i. ∀x Dog(x)∧(∃y Brother(y, x)∧Loves(x, y)) ⇒H appy(x).
ii. ∀x, y Dog(x)∧Brother(y, x)∧Loves(x, y)⇒H appy(x).
(c) (4) (a)(ii) and (a)(iii) both contain disjunctions of two positive literals and hence are not Horn-clause-
representable. (b)(i) and (b)(ii) are logically equivalent; (b)(ii) is obviously Horn, so (b)(i) is too.
5. (8 pts.) Logical Inference
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