Foundations of Probability with Applications

Part I. Foundations of Probability: 1. Necessary and sufficient conditions for existence of a unique measure strictly agreeing with a qualititative probability ordering; 2. Necessary and sufficient qualitative axioms for conditional probability; 3. On using random relations to generate upper and lower probabilities; 4. Conditions on upper and lower probabilities to imply probabilities; 5. Qualitative axioms for random-variable representation of extensive quantifiers; Part II. Causality and Quantum Mechanics: 6. Stochastic incompleteness of quantum mechanics; 7. On the determinism of hidden variable theories with strict correlation and conditional statistical independence of observables; 8. A new proof of the impossibility of hidden variables using the principles of exchangeability and identity of conditional distribution; 9. When are probabilistic explanations possible?; 10. Causality and symmetry; 11. New Bell-type inequalities for N>4 necessary for existence of a hidden variable; 12. Existence of hidden variables having only upper probabilities; Part III. Applications in Education: 13. Mastery learning of elementary mathematics: theory and data.