Suppose Person A believes in [Fact 1]. Is this equivalent to Person A 'operating' with the axiom: "Fact 1 is true" (and any axioms necessitated by Fact 1).
Similarly if Person A states their belief in [Fact 1], Would this be shorthand for Person A stating that they operate on all axioms necessitated by Fact 1 and the axiom "Fact 1 exists"? Is then the purpose of the word 'belief' to be a convenient shorthand for communicating either to oneself or to others what axioms one operates with? (Note: When I say 'operate' what I'm referring to is any mental process of Person A (Reasoning, Algorithmic processes et cetera).
Is recognising/stating belief purposed to reflect objective reality? If not is it meant to reflect the intentions of the 'believer'? What if neither, is the function of recognising/stating belief?