Understand
Part of speech: verb
Definition: To be aware of the meaning of. To believe, based on information. To impute meaning, character etc. that is not explicitly stated. To apply values (axioms).
Acknowledge
Part of speech: verb
Definition: To admit the knowledge of; to recognize as a fact or truth; to declare one's belief in; as, 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 own with gratitude or as a benefit or an obligation; as, to acknowledge a favor.To notify receipt, as of a letter.To own as genuine or valid; to assent to, as a legal instrument, to give it validity; to avow or admit in legal form; as, to acknowledge a deed.