Suppose the agent has progressed to the point shown in Figure 7.4(a), page 239, 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: α 2 = “There is no pit in [2,2].” α 3 = “There is a wumpus in [1,3].” Hence show that KB |= α 2 and KB |= α 3 .

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Answer 1

Textbook Question

Chapter 7, Problem 1E

Suppose the agent has progressed to the point shown in Figure 7.4(a), page 239, 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.

Expert Solution & Answer

Explanation of Solution

True statement

There are eight possible combinations in the three squares.
There are four possibilities for the wumpus location.
KB |= α₂ is true because in every line KB is true and also has α₂ true.
This is similar in the case of α₃.

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Answer 2

Textbook Question

Chapter 7, Problem 1E

Suppose the agent has progressed to the point shown in Figure 7.4(a), page 239, 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.

Expert Solution & Answer

Explanation of Solution

True statement

There are eight possible combinations in the three squares.
There are four possibilities for the wumpus location.
KB |= α₂ is true because in every line KB is true and also has α₂ true.
This is similar in the case of α₃.

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Answer 3

Textbook Question

Chapter 7, Problem 1E

Suppose the agent has progressed to the point shown in Figure 7.4(a), page 239, 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.

Expert Solution & Answer

Explanation of Solution

True statement

There are eight possible combinations in the three squares.
There are four possibilities for the wumpus location.
KB |= α₂ is true because in every line KB is true and also has α₂ true.
This is similar in the case of α₃.

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Answer 4

Textbook Question

Chapter 7, Problem 1E

Suppose the agent has progressed to the point shown in Figure 7.4(a), page 239, 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.

Expert Solution & Answer