1. Introduction to Artificial Intelligence – Unit 5 Inference in first-order logic Course 67842
The Hebrew University of Jerusalem
School of Engineering and Computer Science
Academic Year: 2008/2009

2. Outline
Substitution, Unification MGU
Resolution

9. Examples of Computing MGU (1)
Literal 1: Parents (x, Father(x), Mother (Bill))
Literal 2: Parents (Bill, Father(Bill), y)
Step 1: s = x, t = Bill
variables(s) = true, x is not a variable of t.
We can write:
theta = {[Bill/x]}
Literal 1: Parents (Bill, Father(Bill), Mother (Bill))
And call Unify again.

10. Examples of Computing MGU (1)
Step 2: s = Mother (Bill), t = y
variables(t) = true, y is not a variable of s.
We can write:
theta = {[Bill/x], [Mother (Bill)/y]}
Literal 1: Parents (Bill, Father(x), Mother (Bill))
Literal 2: Parents (Bill, Father(Bill), Mother (Bill))
And we are done.

11. Examples of Computing MGU (2)
Literal 1: g(x,f(x))
Literal 2: g(f(y),y)
Step 1: s = x, t = f(y)
variables(s) = true, x is not a variable of t.
We can write:
theta = {[f(y)/x]}
Literal 1: g(f(y),f(f(y))
And call Unify again.

12. Examples of Computing MGU (2)
Step 2: s = f(f(y)), t = y
s and t share a variable (y) and thus we cannot substitute them.
We got failure !

13. Using Resolution to Prove a Statement

14. Using Resolution to Prove a Statement

17. Converting a Sentence to CNF

18. Converting a Sentence to CNF

19. Converting a Sentence to CNF

20. Converting a Sentence to CNF

21. Converting a Sentence to CNF

22. Converting a Sentence to CNF

23. Converting a Sentence to CNF

24. Converting a Sentence to CNF

25. Converting a Sentence to CNF

26. Converting a Sentence to CNF

27. Skolemization Example

28. Skolemization Example
Original meaning allows each person to fail to love a different animal or to be loved by a different person.
This is also the meaning of (2).
The meaning of (1) is that everyone either fails to love a particular animal A or is loved by some particular animal B.

29. Resolution Example

30. Resolution Example

31. Resolution Example

32. Resolution Example