Mental Model

Can the word belief be replaced with memo, short for MEntal MOdel?

The word I am looking for means "cognitive content that an agent categorizes as true".

Consider a statement X that could potentially be a fact, e.g. "Alice was born in NYC" or "Quebec City is Canada's capital" or "The earth is over 4 billion years old". Which of the following are synonymous? Which are logically connected (so that the truth of one implies the truth of another)?

1. X.
2. X is true.
3. Bob thinks that X.
4. Bob believes X.
5. Bob considers X to be true.
6. Bob holds X to be true.
7. Bob knows X.
8. Bob would bet on X.
9. Bob would bet $100 on X.
10. Bob would bet his house on X.
11. Bob would bet his life on X.
12. Bob claims that X.
13. Bob would say X is true if asked.
14. Bob would say X is true if asked and he had no reason to lie.
15. Bob behaves as if X is true.
16. Bob infers X from other facts he thinks are true.
17. Bob would infer X from other facts he thinks are true.
18. Bob could infer X from other facts he thinks are true.