第七章习题1（人工智能现代方法第四版上册）

Suppose the agent has progressed to the point shown in Figure 7.4(a), page , 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 7.5, 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:
α2
 = “There is no pit in [2,2].”
α3
 = “There is a wumpus in [1,3].”
Hence show that 
KB⊨α2
 and KB⊨α3

解答如下图：

一共有32种情况，第一个方框表示[1,3]，第二个方框表示[2,2]，第三个方框表示[3,3]。

1.没有洞在[2,2]的有第一列和第三列，又因为[2,2]有Breeze,所以[3,1]必须有洞，所以只有第三列，又因为[1,2]只有Stench，所以[1,3]和[2,2]没有洞且两个其中一个有WUMPUS，所以排除掉第三列的1、2、4、6、7、8行，又因为[2,1]只有breeze,所以[2,2]没有WUMPUS,排除掉第三列的第五行，剩第三列第三行一种情况。

2.在[1,3]中有WUMPUS的有第三行和第四行，又因为[1,2]有Stench和[2,1]中有Breeze,所以[3,1]必须有洞且[2,2]没有洞且[1,3]没有洞，剩第三列第三行一种情况。