Suppose we want to use the A* algorithm on the graph below to find the shortest path from node S to node G. Each node is labelled by a capital letter and the value of a heuristic function. Each edge is labelled by the cost to traverse that edge. For this problem: Perform the A* algorithm on this graph, giving your answer in tabular form with headings given in Table below. Indicate the f, g, and h values of each node on the queue as shown in the first two rows of the table. You need not write the contents of the (priority) queue in order in the table. Assume that if you find a path to a node already on the queue that you update its cost (using the lower f value) instead of adding another copy of that node to the queue. IterationNode expandedPriority queue at end of this iteration 0 S = 0 + 6 = 6 (i.e. S = g(S)+h(S) = f(S)) 1SA = 2 + 4 = 6; B = 3+ 4 = 7 ... ... n.. [6]Show the path found by the A* algorithm on the graph above. [2] 10.a) Consider the two following inferences, both of which are logically valid:A:A1. Every student has a smartphone.A2. If every student has a smartphone, then every student can be contacted.A3. Therefore, every student can be contacted.B:B1. Every student has a smartphone.B2. Alice is a student.B3. Therefore, Alice has a smartphone. i. Represent both A and B in First Order Logic (FOL). [4] ii. Translate both A and B into Propositional Logic (PL). [2] iii. Consider the two inferences translated into PL. [4] i. Can A3 (in PL) still be inferred from A1 and A2 (in PL)? (Justify your answer.) ii. Can B3 (in PL) still be inferred from B1 and B2 (in PL)? (Justify your answer.) b) Choose the best knowledge representation method to represent the following knowledge and execute it. Justify your choice. i. Mini is a robin; it lives in a nest, which is on a pine tree in Ms. Wang’s backyard. Robins are birds; they can fly and they have wings. They are an endangered species, and they are protected by government regulations. (5 marks)
Suppose we want to use the A* algorithm on the graph below to find the shortest path from node S to node G. Each node is labelled by a capital letter and the value of a heuristic function. Each edge is labelled by the cost to traverse that edge.
For this problem:
Perform the A* algorithm on this graph, giving your answer in tabular form with headings given in Table below. Indicate the f, g, and h values of each node on the queue as shown in the first two rows of the table. You need not write the contents of the (priority) queue in order in the table.
Assume that if you find a path to a node already on the queue that you update its cost (using the lower f value) instead of adding another copy of that node to the queue.
Iteration
Node expanded
Priority queue at end of this iteration
0
S = 0 + 6 = 6 (i.e. S = g(S)+h(S) = f(S))
1
S
A = 2 + 4 = 6; B = 3+ 4 = 7
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.
.
.
.
.
n
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.
[6]
Show the path found by the A* algorithm on the graph above. [2]
10.
a)
Consider the two following inferences, both of which are logically valid:
A:
A1. Every student has a smartphone.
A2. If every student has a smartphone, then every student can be contacted.
A3. Therefore, every student can be contacted.
B:
B1. Every student has a smartphone.
B2. Alice is a student.
B3. Therefore, Alice has a smartphone.
i. Represent both A and B in First Order Logic (FOL). [4]
ii. Translate both A and B into Propositional Logic (PL). [2]
iii. Consider the two inferences translated into PL. [4]
i. Can A3 (in PL) still be inferred from A1 and A2 (in PL)? (Justify your answer.)
ii. Can B3 (in PL) still be inferred from B1 and B2 (in PL)? (Justify your answer.)
b) Choose the best knowledge representation method to represent the following knowledge and execute it. Justify your choice.
i. Mini is a robin; it lives in a nest, which is on a pine tree in Ms. Wang’s backyard. Robins are birds; they can fly and they have wings. They are an endangered species, and they are protected by government regulations. (5 marks)
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