It not a biggie though IMHO - its basically the same as frequentest and Bayesian type interpretations of Kolmogorov's probability axioms. That said, its still a very important theorem worthy of the praise it received. And guys like Schlosshauer have extended it in an interesting way elucidating...
Savage’s axiomsSmall worldsSeveral axiom systems for preference among acts lead to the existence of a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and the...
We show that two of the axioms used in Piron's representation theorem for quantum mechanics are violated, namely the covering law and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation on the set of properties. ...
In summary, the logical answer “I define as true any statement that can be derived by said rules starting from said axioms” will not satisfy us. (My point is not to criticize this enterprise; only to point that this is not what mathematics is about. I don’t expect any mathematician ...
By imposing that a subject should gamble rationally—which he calls ‘coherence’—Walley then obtains the same axioms as those of a sub- or superadditive expectation operator. Walley's interpretation moreover naturally connects upper and lower expectations with another type of imprecise probabilities ...
A random experiment has sample space S = {a, b, c, d}. Suppose that P ({a, d}) = 3 / 8, P ({a, b}) = 5 / 8, and P ({d}) = 1 / 8. Use the axioms of probability to find the probabilities of each...
Several axiom systems for preference among acts lead to the existence of a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and the subjective probability calculu...
The foreign systems of multi-modal epistemic logic present some pitfalls on epistemological base and the uses of axioms. 国外的多模态认知逻辑系统在认识论基础和公理的使用上存在不足。6) Multi-Modal Logic 多样模态逻辑 1. Hence we propose a kind of structure postulates about the movement of cate...
However, it was unclear if the axioms induce a unique state over time function. In this work, we demonstrate that the previously proposed axioms cannot yield a unique state over time function. In response, we therefore propose an alternative set of axioms that is operationally motivated, and ...
In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference...