Alternative axiomatizations of elementary probability theory.

Alternative axiomatizations of elementary probability theory

1 Outline In this paper I offer some new axiomatizations of elementary (finite) probability theory. The new axiomatizations have the following distinctive features. First, both conditional and unconditional probabilities are simultaneously axiomatized. Second, the axiomatizations are extensions of Kolmogorov probability theory, and have the usual definitions linking conditional and unconditiona...

On qualitative axiomatizations for probability theory

In the literature, there are many axiomatiaations of qualitative probability. They all suffer certain defects: either they are too nonspecific and allow nonunique quantitative interpretations or am overspecific and rule out cases with unique quantitative interpretations. In this paper, it is shown that the class of qualitative probability structures with nonunique quantitative interpretations i...

Elementary Probability Theory in the Eindhoven Style

We extend the Eindhoven quantifier notation to elementary probability theory by adding “distribution comprehensions” to it. Even elementary theories can be used in complicated ways, and this occurs especially when reasoning about computer programs: an instance of this is the multi-level probabilistic structures that arise in probabilistic semantics for security. Our exemplary case study in this...

Radically elementary probability theory , by Edward

Alternative set theory with elementary classes

In this paper we sketch the development and give a model of the formal version of a generalization of the Alternative Set Theory.