|
Last Update: 16 March 2005
Note: |
|
Last Update: 16 March 2005
Note: |
Here is the resolution proof we did in lecture written in the notation of our earlier natural-deduction system assuming that Resolution has been added as a rule of inference. Note: We can then simplify the rule of ¬Elimination to read as follows:
[ ]
1. F
(M ^ P)
2. M
3. P
4. Therefore, F
| 1a. | ¬FvM | : assumption, from 1 |
| 1b. | ¬FvP | : assumption, from 1 |
| 1c. | ¬Mv¬PvF | : assumption, from 1 |
| 2. | M | : assumption, from 2 |
| 3. | P | : assumption, from 3 |
| * 4. | ¬F | : temporary assumption, from 4 |
| * 5. | ¬Mv¬PvF | : send 1c |
| * 6. | ¬Mv¬P | : 1c, 4, Resolution |
| * 7. | M | : send 2 |
| * 8. | ¬P | : 6, 7, Resolution |
| * 9. | P | : send 3 |
| *10. | [ ] | : 8, 9, Resolution |
| *11. | F | : 4, 10, ¬Elim |
| 12. | F | : return 11 |
or 
material is highlighted