What is the meaning of the word "acknowledge"?

Definitions:

to accept as legally binding and valid verb
- Please acknowledge the deed so that I can go home.
to accept someone to be what is claimed or accept his power and authority verb
- The Crown Prince was acknowledged as the true heir to the throne.
to declare to be true or admit the existence or reality or truth of verb
- I didn't want to acknowledge their deity.
to express obligation, thanks, or gratitude for something verb
- We must acknowledge the kindness they showed towards us.
to express recognition of the presence or existence of, or acquaintance with verb
- They never acknowledge their colleagues when they run into each other in the hallway.
to report the receipt of verb
- The program committee acknowledged the submission of the authors of the paper.