MSC IN FINANCE – FINANCIAL INFORMATICS PLANNING MOVES ON

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In the game of chess, a knight can legally move two squares (on the chessboard) either horizontally or vertically, followed by one square in an orthogonal direction as long as the knight does not move off the board

MSc in Finance – Financial Informatics

Planning Moves on a Chessboard

In the game of chess, a knight can legally move two squares (on the chessboard) either horizontally or vertically, followed by one square in an orthogonal direction as long as the knight does not move off the board.


(a) Consider a 3x3 chessboard with squares labelled from 1 to 9:


1

2

3

4

5

6

7

8

9


Describe productions or production rules representing all possible moves of a knight on the 3x3 chessboard. The antecedent of any given production should indicate initial state and the consequent the goal state.


(a) The productions for the knight’s legal move on a 3x3 chessboard are:


RULE

1 If kt on 1 then move kt to 8

2 If kt on 1 then move kt to 6

3 if kt on 2 then move kt to 9

4 if kt on 2 then move kt to 7

5 if kt on 3 then move kt to 4

6 if kt on 3 then move kt to 8

7 if kt on 4 then move kt to 9

8 if kt on 4 then move kt to 3

9 if kt on 6 then move kt to 1

10 if kt on 6 then move kt to 7

11 if kt on 7 then move kt to 2

12 if kt on 7 then move kt to 6

13 if kt on 8 then move kt to 3

14 if kt on 8 then move kt to 1

15 if kt on 9 then move kt to 2

16 if kt on 9 then move kt to 4



  1. The 3x3 (chessboard) knight’s tour problem requires that, if possible, a solution be found for moving a knight from one square to another. Describe a production system that will help in solving the 3x3 knight tour problem. Describe how the production system will resolve conflicts it may find in the system’s knowledge base of the knight’s legal moves.


The 3x3 (chessboard) knight’s tour problem requires that, if possible, a solution be found for moving a knight from one square to another. Describe a production system that will help in solving the 3x3 knight tour problem. Describe how the production system will resolve conflicts it may find in the system’s knowledge base of the knight’s legal moves.



The production system should comprise:


(i) Working memory that contains both the initial state and goal state

(ii) A set of productions describing the knight’s legal moves

(iii) An interpreter which applies rules until the current state equals the goal state and then halts.

(iv) Conflict results in strategy which uses first match that does not lead to a loop.


  1. On the 3x3 chessboard shows above, a knight is placed on the square labelled 1 and you have to move the knight to the square labelled 2. Use the production system to complete this move and tabulate for each production cycle, the contents of the working memory, the conflict set and the rule which was fired.


Cycle

Working Memory

Conflict Set

Fire Rule


Initial State

Goal State



0

1

2

1, 2

1

1

8

2

13, 14

13

2

3

2

5, 6

5

3

4

2

7, 8

7

4

9

2

15, 16

7

5

2

2

-

Halt




(d) What happens if the knight is placed in the square labelled 5?


The knight cannot be placed on the square labelled 5 because any move from here will make it illegally go off the chessboard.



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