acknowledge

verb

• To admit the knowledge of; to recognize as a fact or truth; to declare one's belief in

  "to acknowledge the being of a god"

• To own or recognize in a particular quality, character or relationship; to admit the claims or authority of; to give recognition to.
• To be grateful of (e.g. a benefit or a favour)

  "to acknowledge a favor"

• To report (the receipt of a message to its sender).

  "This is to acknowledge your kind invitation to participate in the upcoming debate."

• To own as genuine or valid; to assent to (a legal instrument) to give it validity; to avow or admit in legal form.