Axioms of belief

What is belief? Some (many?) people think that belief is entirely synonymous with faith. For example, some theists say that if an atheist has no faith then they believe in nothing. I'm an atheist, and I definitely have beliefs that I believe have nothing to do with faith. (There, that was one of them.)

To my understanding, belief and faith have very different connotations, but when I look up these words in a dictionary, I find it's not too surprising that people consider them to be equivalent. For example if you read the definitions given for these words in dictionary.com you'll find one definition of faith is: a religious belief, and one definition of belief is: a religious tenet or tenets. With just these definitions, any reasonable person would have to conclude that belief and faith are essentially synonymous.

But I still assert that they are not. And I further assert that by allowing them to be synonyms, we muddy the debate between faith and reason. I propose that we make it clear that faith is a subset of belief. I like this definition from wikipedia: Belief is the psychological state in which an individual is convinced of the truth of a proposition.

Given this definition, religious faith is clearly a form of belief. However, it is a restricted form. It is restricted in both the nature of the proposition that is made, and in the manner that the believer is convinced. The proposition is a theological one made about the possibility of something supernatural. The believer is convinced of the proposition not because of objective evidence, but because of subjective feelings and the testimony of others.