How can you say counter-positive in Vietnamese
Name of the rule for negating quantifiers
Many rules of logic have accepted names:
- $ \ neg (P \ lor Q) \ iff (\ neg P) \ land (\ neg Q) $ and $ \ neg (P \ land Q) \ iff (\ neg P) \ lor (\ neg Q) $ Called "De Morgan's Rules" (or "Laws").
- $ (P \ lor Q) \ land R \ iff (P \ land Q) \ lor (P \ land R) $ is called "distributability".
- $ (P \ to Q) \ iff (\ neg Q \ to \ neg P) $ is called "transposition" or "replace with the contrapositive".
But what about the rules for manipulating quantifiers?
- $ \ neg (\ forall x: P (x)) \ iff \ exists x: \ neg P (x) $
- $ \ neg (\ exists x: P (x)) \ iff \ forall x: \ neg P (x) $
Did these rules accept names in English?
When negating statements with quantifiers, @ Bram28 calls this the "dagger rule", but a quick Google search didn't find great textual support for that name.
In Why is the universal quantifier negated there is an existential quantifier? It is believed that it is appropriate to follow this rule as an axiom formal logic, but I want to know, "What axiom is that?" :) :)
In A proof of $ (\ forall x P (x)) \ to A) \ Rightarrow \ exists x (P (x) \ to A) $ the questioner uses it in a formal proof under the name "A Known Identity", which is just beautiful. :) :)
I'm looking for a name so I can use it in a blog post where I first introduce the rule and say, "This is called the rule of Foo." And then further down I would say, "Now let's apply the rule." by Foo to translate this statement into ... "
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