The purpose of the Declaration of Independence, of course, was to announce to the world and to the American people (and, of course, to King George and Parliament) that the United States deemed itself a free and independent nation. I will argue that the document was based on two major premises. One was that a declaration itself could effect such a change. As historian Lynn Hunt has pointed out in her book Inventing Human Rights, the word "declaration" carried powerful connotations in English. Most of the major political documents in English history had been "petitions" or "bills," words which signified a certain amount of deference. Of course, the colonies still had a military struggle to win, but the point stands.
Another major assumption or premise is spelled out in the Declaration. This is that all men have certain rights which cannot be taken away by government without their consent. From this, the document proceeds to a sort of Lockean conclusion that only governments that have the protection of these rights as an end were legitimate. Because, in the view of the colonists, the British government had violated these "unalienable" rights, the colonists claimed the right to separate. The premise, again, was that people were possessed of these rights in the first place.