Exercise 7.1

Suppose the agent has progressed to the point shown in Figure wumpus-seq35-figure(a), page wumpus-seq35-figure, having perceived nothing in [1,1], a breeze in [2,1], and a stench in [1,2], and is now concerned with the contents of [1,3], [2,2], and [3,1]. Each of these can contain a pit, and at most one can contain a wumpus. Following the example of Figure wumpus-entailment-figure, construct the set of possible worlds. (You should find 32 of them.) Mark the worlds in which the KB is true and those in which each of the following sentences is true:

$\alpha_2$ = “There is no pit in [2,2].”

$\alpha_3$ = “There is a wumpus in [1,3].”

Hence show that ${KB} {\models}\alpha_2$ and ${KB} {\models}\alpha_3$.