1. Artificial Intelligence
Lecture 5

2. Clause
Is a representation of facts where different literals have disjunctive relation
Typesground clause and horn clause
Ground clausewithout any variable
Example a()
Horn clause at most one positive clause
Examplea(x,y)

3. Considerations for clauses
A given relation can have any number of objects
A predicate can have any number of arguments including zero.
Number of arguments  arity
An object name can represent a physical entity(Bob,automobile)/an abstract concept(defective)
Can be noun , adverb or adjective
Objects must be singular
Names reserved for prolog should not be used as object name

4. Steps for converting propositional logic to causal form

5. Steps for conversion in elaborated form

6. Steps for conversion in elaborated form(Cont..)

7. Steps for conversion in elaborated form(Cont..)

8. Skolemisation Is the process of eliminating existential quantifier
Steps of skolemisation

9. Resolution
Is the process of proving theorem based on some clauses

10. Types of resolution Unit resolution Binary resolution
Linear resolution

11. Definition of different types of resolution

12. Algorithm on Resolution

14. Example
1. Ravi likes all kind of food. 2. Apples and chicken are food 3. Anything anyone eats and is not killed is food 4. Ajay eats peanuts and is still alive 5. Rita eats everything that Ajay eats Prove that Ravi likes peanuts using resolution.

15. Step 1: Converting the given statements into Predicate/Propositional Logic
i. ∀x : food(x) → likes (Ravi, x)
ii. food (Apple) ^ food (chicken)
iii. ∀a : ∀b: eats (a, b) ^ ~ killed (a) → food (b)
iv. eats (Ajay, Peanuts) ^ alive (Ajay)
v. ∀c : eats (Ajay, c) → eats (Rita, c)
vi. ∀d : alive(d) → ~killed (d)
vii. ∀e: ~killed(e) → alive(e)
Conclusion: likes (Ravi, Peanuts)

16. Step 2: Convert into Clausal form
i. ~food(x) v likes (Ravi, x)
ii. Food (apple)
iii. Food (chicken)
iv. ~ eats (a, b) v killed (a) v food (b)
v. Eats (Ajay, Peanuts)
vi. Alive (Ajay)
vii. ~eats (Ajay, c) V eats (Rita, c)
viii. ~alive (d) v ~ killed (d)
ix. Killed (e) v alive (e)

17. Step 3: Negate the conclusion
~ likes (Ravi, Peanuts)

18. Step 4: Resolve using a resolution tree