A belief system is a personal logical system. Logical systems themselves are sets of axioms, nothing more.
Crucial is the distinction between axioms and values. Axioms are descriptive while values are normative. Unlike axioms, values are preferential focus points in your own life and therefore subjective. Since values are subjective, it follows that values have no place in a belief system insofar that belief systems are personal logical systems.
The proper way to develop a belief system is a two-step process:
I will consider various examples of belief systems. At the end of this page, I attached an example of a potential Simple Pragmatist belief system.
Simple Pragmatism in particular only has one axiom: