General Antonyms:
* Ignore: To pay no attention to.
* Disregard: To treat as unimportant.
* Overlook: To fail to notice or consider.
* Dismiss: To reject or refuse to consider.
* Deny: To refuse to admit the truth of something.
Antonyms related to specific meanings of "acknowledge":
* Refute: To prove something to be false or incorrect (when acknowledging a claim or argument).
* Disavow: To deny responsibility for or connection to something (when acknowledging responsibility or involvement).
* Conceal: To hide or keep secret (when acknowledging something known).
* Suppress: To prevent something from being known or expressed (when acknowledging something publicly).
The best antonym will depend on the specific situation.