Conditional proof for multiple quantifier

MHB
Thread starter lize
Start date Mar 7, 2016
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Conditional Multiple Proof

In summary, conditional proof for multiple quantifier is a logical method used to prove a conditional statement with multiple quantifiers. It involves assuming the antecedent and deriving the consequent under that assumption. It differs from regular conditional proof in that it deals with more than one quantifier, requiring assumptions for each quantifier. The benefit of using this method is that it allows for the systematic and organized proof of complex statements involving multiple quantifiers. However, there are restrictions, such as the antecedent being a conjunction of quantifiers and the consequent being a conditional statement with the same quantifiers. This method can be used in all logical systems that allow for quantifiers and conditional statements, making it universally applicable in fields such as mathematics, computer

Mar 7, 2016

lize

Hi, I don't know how to prove ((Ǝx) F(x) →(Ǝx) (G(x)) with conditional proof from:
((Ǝx) F(x) → (∀z) H(z))
H(a) →G(b)

Thanks

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Mar 13, 2016

Evgeny.Makarov

Gold Member

MHB

What kind of proof do you have in mind? If you are talking about a formal proof in some logical calculus, then please see https://driven2services.com/staging/mh/index.php?threads/29/.

Related to Conditional proof for multiple quantifier

1. What is conditional proof for multiple quantifier?

Conditional proof for multiple quantifier is a logical method used to prove a conditional statement that contains multiple quantifiers, such as "for all" or "there exists." It involves assuming the antecedent of the conditional statement and deriving the consequent under that assumption.

2. How is conditional proof for multiple quantifier different from regular conditional proof?

Regular conditional proof only involves a single quantifier, while conditional proof for multiple quantifier deals with more than one quantifier. This means that in conditional proof for multiple quantifier, we have to make assumptions for each quantifier and derive the consequent accordingly.

3. What is the benefit of using conditional proof for multiple quantifier?

Conditional proof for multiple quantifier allows us to prove complex conditional statements that involve multiple quantifiers in a systematic and organized way. It also helps us to better understand the relationship between the quantifiers and the consequent of the conditional statement.

4. Are there any restrictions on using conditional proof for multiple quantifier?

Yes, there are certain restrictions when using conditional proof for multiple quantifier. The antecedent of the conditional statement must be a conjunction of the quantifiers, and the consequent must be a conditional statement with the same quantifiers. Additionally, the scope of each quantifier must be clearly defined.

5. Can conditional proof for multiple quantifier be used in all logical systems?

Yes, conditional proof for multiple quantifier can be used in all logical systems that allow for the use of quantifiers and conditional statements. It is a universally applicable method in logic and is commonly used in various fields such as mathematics, computer science, and philosophy.