While many theories in cognitive science rely on the concept of a "belief" I do not see much on the definition of a belief or how it compares to other mental states. What is a belief, and how does it compare to things like opinions?
Edit: This article from the Guardian reviews research into what forms and influences belief, gives some make up of what a belief is, but I could not find a, and separate, scientific defintion.
A opinion is a judgement based on facts while a belief is a conviction based on personal values.
An opinion is a judgment based on facts, an honest attempt to draw a reasonable conclusion from factual evidence. (For example, we know that millions of people go without proper medical care, and so you form the opinion that the country should institute national health insurance even though it would cost billions of dollars.) An opinion is potentially changeable--depending on how the evidence is interpreted. By themselves, opinions have little power to convince. You must always let your reader know what your evidence is and how it led you to arrive at your opinion.
Unlike an opinion, a belief is a conviction based on cultural or personal faith, morality, or values. Statements such as "Capital punishment is legalized murder" are often called "opinions" because they express viewpoints, but they are not based on facts or other evidence. They cannot be disproved or even contested in a rational or logical manner. Since beliefs are inarguable, they cannot serve as the thesis of a formal argument.