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The prenex normal form can now be obtained by moving all quantifiers to the front of the formula. To accomplish Step 1 (eliminate the \u2192,\u2194), make use of the following logical equivalences: A \u2192 B |=| ¬A \u2228 B. A \u2194 B |=| (¬A \u2228 B)
Reduction to Skolem normal form is a method for removing existential quantifiers from formal logic statements, often performed as the first step in an automated theorem prover.
The rules for conversion to prenex normal form then are as follows: \u2022 If you have a subformula of the form ¬(Qx A) then replace it by Qx ¬A. If you have a subformula of the form ((Qx A) \u2227 B) then replace it by Qx1(A1 \u2227 B), where x1 is a new variable not occurring in the given formula and A1 = A[x | x1].
A formula of the predicate calculus is in prenex normal form (PNF) if it is rewritten as a string of quantifiers and bound variables, called the prefix, followed by a quantifier-free part, called the matrix.
There are two types of quantifier in predicate logic - Existential Quantifier and Universal Quantifier.

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The rules for conversion to prenex normal form then are as follows: \u2022 If you have a subformula of the form ¬(Qx A) then replace it by Qx ¬A. If you have a subformula of the form ((Qx A) \u2227 B) then replace it by Qx1(A1 \u2227 B), where x1 is a new variable not occurring in the given formula and A1 = A[x | x1].
A formula of the predicate calculus is in prenex normal form (PNF) if it is rewritten as a string of quantifiers and bound variables, called the prefix, followed by a quantifier-free part, called the matrix.
Skolemization is the replacement of strong quantifiers in a sequent by fresh function symbols, where a strong quantifier is a positive occurrence of a universal quantifier or a negative occurrence of an existential quantifier. Skolemization can be considered in the context of either derivability or satisfiability.
In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a cluster concept. As a normal form, it is useful in automated theorem proving.
Skolemization in Artificial Intelligence is a procedure used when there is a requirement of the reduction of any first-order formula to its Skolem normal form. This is usually done when there is a need for proving a theorem by using programming.

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