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.
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.
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter9: Integer Programming
Section9.2: Formulating Integer Programming Problems
Problem 14P
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Question
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.
![a2
KB
KB
(b)
(a)
Figure 7.5 Possible models for the presence of pits in squares [1,2], [2,2), and [3,1]. The
KB corresponding to the observations of nothing in [1,1] and a breeze in [2,1] is shown by
the solid line. (a) Dotted line shows models of a1 (no pit in [1,2]). (b) Dotted line shows
models of a2 (no pit in [2,2]).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46c1c726-4f08-4fc5-8983-c61c7b75d341%2F92e2d0d9-97eb-49aa-92db-c4878733b369%2Fduazw6s_processed.png&w=3840&q=75)
Transcribed Image Text:a2
KB
KB
(b)
(a)
Figure 7.5 Possible models for the presence of pits in squares [1,2], [2,2), and [3,1]. The
KB corresponding to the observations of nothing in [1,1] and a breeze in [2,1] is shown by
the solid line. (a) Dotted line shows models of a1 (no pit in [1,2]). (b) Dotted line shows
models of a2 (no pit in [2,2]).
![= Agent
= Breeze
1,4
2,4
3,4
4,4
1,4
2,4
3,4
4,4
B
= Glitter, Gold
OK = Safe square
= Pit
G
1,3
2,3
3,3
4,3
1,3
2,3
3,3
4,3
= Stench
V = Visited
w = Wumpus
S
3,2
4,2
2,2
P?
3,2
1,2
2,2
1,2
4,2
OK
OK
2,1
3,1
4,1
1,1
2,1
A
3,1
P?
1,1
4,1
V
B
OK
OK
OK
OK
(a)
(b)
Figure 7.3
uation, after percept [None, None, None, None, None]. (b) After one move, with percept
(None, Breeze, None, None, None].
The first step taken by the agent in the wumpus world. (a) The initial sit-
1,4
2,4
4,4
A
1,4
2,4
P?
3,4
4,4
3,4
= Agent
= Breeze
= Glitter, Gold
OK = Safe square
B
G
1,3
W!
4,3
1,3
W!
2,3
A
4,3
2,3
3,3
3,3
P?
= Pit
= Stench
V = Visited
W = Wumpus
P
S
S G
B
1,2
A
2,2
3,2
4,2
1,2
S
2,2
4,2
3,2
S
V
V
OK
OK
ок
OK
1,1
2,1
B
3,1
P!
4,1
1,1
2,1
3,1
P!
4,1
V
V
V
V
OK
OK
OK
OK
(a)
(b)
Figure 7.4
with percept (Stench, None, None, None, None]. (b) After the fifth move, with percept
(Stench, Breeze, Glitter, None, None].
Two later stages in the progress of the agent. (a) After the third move,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46c1c726-4f08-4fc5-8983-c61c7b75d341%2F92e2d0d9-97eb-49aa-92db-c4878733b369%2Fgzfq6z_processed.png&w=3840&q=75)
Transcribed Image Text:= Agent
= Breeze
1,4
2,4
3,4
4,4
1,4
2,4
3,4
4,4
B
= Glitter, Gold
OK = Safe square
= Pit
G
1,3
2,3
3,3
4,3
1,3
2,3
3,3
4,3
= Stench
V = Visited
w = Wumpus
S
3,2
4,2
2,2
P?
3,2
1,2
2,2
1,2
4,2
OK
OK
2,1
3,1
4,1
1,1
2,1
A
3,1
P?
1,1
4,1
V
B
OK
OK
OK
OK
(a)
(b)
Figure 7.3
uation, after percept [None, None, None, None, None]. (b) After one move, with percept
(None, Breeze, None, None, None].
The first step taken by the agent in the wumpus world. (a) The initial sit-
1,4
2,4
4,4
A
1,4
2,4
P?
3,4
4,4
3,4
= Agent
= Breeze
= Glitter, Gold
OK = Safe square
B
G
1,3
W!
4,3
1,3
W!
2,3
A
4,3
2,3
3,3
3,3
P?
= Pit
= Stench
V = Visited
W = Wumpus
P
S
S G
B
1,2
A
2,2
3,2
4,2
1,2
S
2,2
4,2
3,2
S
V
V
OK
OK
ок
OK
1,1
2,1
B
3,1
P!
4,1
1,1
2,1
3,1
P!
4,1
V
V
V
V
OK
OK
OK
OK
(a)
(b)
Figure 7.4
with percept (Stench, None, None, None, None]. (b) After the fifth move, with percept
(Stench, Breeze, Glitter, None, None].
Two later stages in the progress of the agent. (a) After the third move,
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