Thomas Marlow
Published 2006-03-08, updated 2006-10-12Version 3
We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these generalised probabilities as partially ordered notions of preference and we introduce a tentative generalised notion of Shannon entropy. A Bayesian approach to probability theory is adopted throughout, thus the axioms we use will be minimal criteria of rationality rather than ad hoc mathematical axioms.
Comments: 14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published version
Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem
Probability distributions and Gleason's Theorem
Quantum probabilities from combination of Zurek's envariance and Gleason's theorem
