Artificial Intelligence Lecture 5

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)

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

Steps for converting propositional logic to causal form

Steps for conversion in elaborated form

Steps for conversion in elaborated form(Cont..)

Steps for conversion in elaborated form(Cont..)

Skolemisation Is the process of eliminating existential quantifier Steps of skolemisation

Resolution Is the process of proving theorem based on some clauses

Types of resolution Unit resolution Binary resolution Linear resolution

Definition of different types of resolution

Algorithm on Resolution

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.

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)

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)

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

Step 4: Resolve using a resolution tree