Question

1.Indicate which of the following Prolog constructs correctly state, "All squares adjacent to a wumpus have a stench."

		stench(X) :-     adjacentToWumpus(X).
		stench(X) :-     square(X),     adjacentToWumpus(X).
		square(X) :-     adjacentToWumpus(X),     stench(X).
		adjacentToWumpus(X) :-     square(X),     stench(X).

2.When the expression:

∀x∃y (Man(x) ∧ Object(y) ⇒ Desires(x, y))

is converted to:

∀x(Man(x) ∧ Object(F(y)) ⇒ Desires(x, F(y)))

what is F(y)?

		a ground term
		a unifier
		a Skolem function
		unknown

3.Given the following knowledge base:

Knows(John, Jane)
Knows(John, Bill)
Wealthy(y)
Greedy(Jane)
Generous(Bill)

which of the following unifications will result in a substitution that satisfies the query, "Who does John know who is greedy?" (select all that apply):

		UNIFY(Knows(John, Greedy(x)), Knows(John, y))
		UNIFY(Knows(John, Greedy(x)), Knows(John, Bill))
		UNIFY(Knows(John, Greedy(x)), Wealthy(y))
		UNIFY(Knows(John, Greedy(x)), Knows(y, Greedy(Jane))
		UNIFY(Knows(John, Greedy(x)), Generous(y))

4.What name is given to a literal value substituted for a variable in an expression that uses a universal quantifier?

		Skolem constant
		substitution
		answer literal
		ground term

Answer 1

1. Option D is correct.

Option A is incorrect. The construct says that X has stench if X is adjacent to Wumpus. The construct doesn't state what X is. There could be stench in other squares also.

Option B is incorrect because the construct says that X has stench if it is a square and if it is adjacent to Wumpus. But the statement in the question says that all squares adjacent to Wumpus have stench but not vice versa.

Option C is incorrect because the construct says that X is a square if it has stench and if it is adjacent to Wumpus.

Option D is correct because the construct says the X is adjacent to Wumpus if it is a square and if it has stench. This is clearly conveyed from the input statement.

2.Option C is correct.

Option A is incorrect because a ground term doesn't contain any variable.

Option B is incorrect because a unifier makes two atoms resolvable.

Option C is correct because a Skolem function f(y) can replace every existentially quantified variable y.

Option D is incorrect because f(y) is a Skolem function.

3. Option A and D are correct.

Option A is correct because it is of the form of a most general unifier that resolves to Greedy(x)/y

Option B is incorrect because it resolves to Greedy(x)/Bill but according to our knowledge base Bill is generous.

Option C is incorrect because Knows and Wealthy cannot be unified

Option D is correct because it resolves to a redundant unification i.e., Greedy(x)/Greedy{Jane) and y/John

Option E is incorrect because Knows and Generous cannot be unified.

4 Option C is correct.

Option A is incorrect because Skolem constant replaces existential quantifiers.

Option B is incorrect because substitution can be used to replace sub-expressions or variables or terms.

Option C is correct because a literal is an atomic formula or its negation.

Option D is incorrect because a ground term doesn't contain any variables.