1. 1CS3754 Class Notes 14B, John Shieh, 2013

2. 2

3. 3 Figure 2.5: Further steps in the unification of (parents X (father X) (mother bill)) and (parents bill (father bill) Y). CS3754 Class Notes 14B, John Shieh, 2013

4. Resolution refutation proofs involve the following steps: 4CS3754 Class Notes 14B, John Shieh, 2013

5. Clausal Form 5CS3754 Class Notes 14B, John Shieh, 2013

6. Algorithm to convert to clausal form (1) 6CS3754 Class Notes 14B, John Shieh, 2013

7. Algorithm to convert to clausal form (2) 4. Eliminate existential quantifiers, by using Skolem functions, named after the Norwegian logician Thoralf Skolem. e.g., ( ∃ X) L(X) is replaced by L(a) ( ∃ X) ( ∃ Y) L(X, Y) is replaced by ( ∃ X) L(X, f(X)) 5. Convert the WFF to prenex form which is a sequence of quantifiers followed by a matrix. 6. Convert the matrix to conjunctive normal form, which is a conjunctive of clauses. Each clause is a disjunction. 7. Drop the universal quantifiers. 8. Eliminate the conjunctive signs by writing the WFF as a set of clauses 9. Rename variables in clauses, if necessary, so that the same variable name is only used in one clause. 7CS3754 Class Notes 14B, John Shieh, 2013

8. Fig 13.3Resolution proof for the “dead dog” problem. 8CS3754 Class Notes 14B, John Shieh, 2013

9. Fig 13.4One resolution proof for an example from the propositional calculus. 9CS3754 Class Notes 14B, John Shieh, 2013

10. 10 CS3754 Class Notes 14B, John Shieh, 2013

11. Fig 13.5One refutation for the “happy student” problem. 11CS3754 Class Notes 14B, John Shieh, 2013

12. 12CS3754 Class Notes 14B, John Shieh, 2013

13. Fig 13.6Resolution proof for the “exciting life” problem. 13CS3754 Class Notes 14B, John Shieh, 2013

14. Fig 13.8Complete state space for the “exciting life” problem generated by breadth-first search (to two levels). 14CS3754 Class Notes 14B, John Shieh, 2013

15. Fig 13.7another resolution refutation for the example of Fig 13.6. 15CS3754 Class Notes 14B, John Shieh, 2013

16. Fig 13.9Using the unit preference strategy on the “exciting life” problem. 16CS3754 Class Notes 14B, John Shieh, 2013

17. Fig 13.10 Unification substitutions of Fig 13.6 applied to the original query. 17CS3754 Class Notes 14B, John Shieh, 2013

18. Fig 13.11 Answer extraction process on the “finding fido” problem. 18CS3754 Class Notes 14B, John Shieh, 2013

19. Fig 13.12 Skolemization as part of the answer extraction process. 19CS3754 Class Notes 14B, John Shieh, 2013