to accept, admit, or recognize something, or the truth or existe

http://dictionary.cambridge.org/dictionary/british/acknowledge

acknowledge: to accept, admit, or recognize something, or the truth or existence of something.

[+ -ing verb] She acknowledged having been at fault.

[+ that] She acknowledged that she had been at fault.

You must acknowledge the truth of her argument.

Historians generally acknowledge her as a genius in her field.

[+ obj + to infinitive ] She is usually acknowledged to be one of our best artists.

They refused to acknowledge (= to recognize officially) the new government.

He didn't even acknowledge my presence (= show that he had seen me).

The government won't even acknowledge the existence of the problem.