I understand that [All] statements negate to a [Some, Not] statement

(All cats are pretentious) negates to (Some cats are not pretentious)

Following this, [Some] statements negate to [None]

(Some cats are pretentious) negates to (No cats are pretentious)

The question I am seeking clarification on is for negating [Some, Not] statements; does [Some, Not] negate back to [All]?

(Some dogs are not brave) negates to (All dogs are brave)?

Thank you for the help.