What is the solution method of toe-in paradigm?

Solution method of front-end paradigm: 1. Use quantifier conversion to put negation in front of the atomic predicate formula; 2. Use renaming rules and substitution rules to use different symbols for all variables in the formula; 3. Use the expansion of quantifier scope to move the quantifier to the front.

Solution method of toe-in paradigm:

Concept of toe-in paradigm:

A formula, if the quantifiers are at the beginning of the full formula and their scope extends to the end of the entire formula, the formula is called Prenex Normal Form.

The front bundle paradigm can be recorded as the following Q form

where Qi is any or existence, xi is the individual variable, and A is the predicate without quantifier formula.

If A is a conjunctive normal form, then P is called a prefixed conjunctive normal form; if A is a disjunctive normal form, then P is called a prefixed disjunctive normal form.

Any predicate can be formulated into front-end normal form by using renaming rules, substitution rules, negation formulas of quantifiers, and expansion and contraction formulas of quantifier scope.

PS: If a formula contains only A alone, then the formula is also in forward normal form.

Method to find the prefix normal form:

(1) Eliminate the connectives -> and ;;

(2) Use quantifier conversion to put negation in front of the atomic predicate formula, that is, use quantifier conversion formula to put the negative connective in front of proposition variables and predicate fill-ins;

(3) Use renaming rules and substitution rules to use different symbols for all variables in the formula;

(4) Use the expansion and contraction law of quantifier scope to move the quantifier forward , that is, using the expansion of the quantifier scope to move the quantifier to the front.

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