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If we convert

$\exists u \forall v \forall x \exists y (P(f(u), v, x, y) \rightarrow Q(u,v,y))$ to $\forall v \forall x (P(f(a), v, x, g(v,x)) \rightarrow Q(a,v,g(v,x)))$.

This process is known as

  1. Simplification
  2. Unification
  3. Skolemization
  4. Resolution
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Let us go through each option:

1. Simplification: Make sentence simple eg: ~(~P)= P

2.  Unification: Combine 2 sentences, replace variables with constants from each sentence, and simplify

  • Sentence1: parents(x, father(x), mother(Bill))  
  • Sentence  2: parents(Bill, father(Bill), y)
  • Unification Result: {x/Bill, y/mother(Bill)}

3. Skolemization : Removing all the existential quantifiers in a sentence with equivalent functions. Eg: (∃u) (∀v)P(f(u), v) is converted into  (∀v)P(f(a), v)

4. Resolution: Deriving all possible combinations of given axiom and check whether they are true/false for goal statement. P|=Q

Answer of given question will be (C) Skolemization :

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Ans is C  here all existential quantifiers are removed and process of removing existential quantifier is called SKOLEMIZATION
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Answer: C

Conversion of sentences FOL to CNF requires skolemization.

“Skolemization” is a transformation on first-order logic formulae, which removes all existential quantifiers from a formula. 
 

Skolemization Idea: 
Remove existential quantifiers by introducing new function symbols.
 

Skolemization Algorithm: 
Remove existential quantifiers and For each existentially quantified variable introduce a n-place function where n is the number of previously appearing universal quantifiers(before the removed existential quantifier).
Special case when no previous universal quantifier: introduce constants.
 

Three Practice Questions in the following PDF:

https://www.cs.toronto.edu/~sheila/384/w11/Lectures/csc384w11-KR-tutorial.pdf 

Try the following question:

Answer:

For Q1, Answer is A.

For Q2, Answer is A.

Answer:

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