Run this with clingo to see examples of non-monotonicity in ASP.
suduko_rules demonstrates how to declaratively define the rules of Sudoku, and in turn, create a solver for the game. sudoku_example_game1 is an example of the game depicted below, where the bold numbers are the initial hints of the game defined in the program:
| 5 | 6 | 3 | 2 | 1 | 9 | 8 | 4 | 7 |
| 7 | 1 | 8 | 4 | 5 | 3 | 9 | 2 | 6 |
| 2 | 9 | 4 | 6 | 7 | 8 | 3 | 1 | 5 |
| 1 | 2 | 5 | 7 | 9 | 6 | 4 | 3 | 8 |
| 6 | 8 | 7 | 3 | 4 | 2 | 1 | 5 | 9 |
| 3 | 4 | 9 | 1 | 8 | 5 | 7 | 6 | 2 |
| 4 | 5 | 1 | 8 | 2 | 7 | 6 | 9 | 3 |
| 9 | 7 | 6 | 5 | 3 | 1 | 2 | 8 | 4 |
| 8 | 3 | 2 | 9 | 6 | 4 | 5 | 7 | 1 |
Appending it to suduko_rules should generate the matching model answer.
sudoku_example_game2 defines three sections of the game. When running that with clingo, you should be able to enumerate all possible games for the following:
| 5 | 6 | 3 | ||||||
| 7 | 1 | 8 | ||||||
| 2 | 9 | 4 | ||||||
| 7 | 9 | 6 | ||||||
| 3 | 4 | 2 | ||||||
| 1 | 8 | 5 | ||||||
| 6 | 9 | 3 | ||||||
| 2 | 8 | 4 | ||||||
| 5 | 7 | 1 |
This should generate 133,467 different solutions.