One of the most obvious contradictions found in both the Declaration of Independence and the Bill of Rights is the fact that neither document acknowledges the problem that slavery presents.
The Declaration of Independence states that the United States is a "free" country. It also highlights the negatives of being a subject to Great Britain. The colonists refuse to be subjects because they recognize the importance of freedom for a person. However, they fail to recognize that this liberty is equally important to the slaves who do not enjoy it.
On the other hand, the Bill of Rights states many of the rights and protections that American citizens enjoy. Nevertheless, it fails to understand that for these protections to be significant, they should also be granted to African Americans.
As opposed to stating that there are logical inconsistencies inside the Independence Declaration, it is increasingly exact to state that there are variances between the expressions of the Independence Declaration and the activities of the individuals who marked it.
The principle logical inconsistency is in the possibility that all men are made equivalent and that they have the natural right to "life, freedom, and the quest for satisfaction. However, this was not a contradiction itself.