The logic of uncertainty as a logic of experience and chance and the co~event-based Bayes' theorem

TL;DR

This paper introduces a new co~event-based logic of uncertainty that unifies experience and chance, demonstrating its effectiveness through a Bayesian scheme example and aiming to bridge Bayesian and frequentist debates.

Contribution

It develops a novel co~event axiomatics and applies it to the logic of uncertainty, offering a new perspective on Bayesian and frequentist approaches.

Findings

Effective co~event splitting of Bayesian logic demonstrated

New theory bridges Bayesian and frequentist debates

Provides a unified framework for experience and chance

Abstract

The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called co~event. The theory of experience and chance is the theory of co~events. To study the co~events, it is not enough to study the experience and to study the chance. For this, it is necessary to study the experience and chance as a single entire, a co~event. In other words, it is necessary to study their interaction within a co~event. The new co~event axiomatics and the theory of co~events following from it were created precisely for these purposes. In this work, I am going to demonstrate the effectiveness of the new theory of co~events in a studying the logic of uncertainty. I will do this by the example of a co~event splitting of the logic of the Bayesian scheme, which has a long history of fierce debates between Bayesianists and frequentists. I hope the logic of the theory of experience and chance will make its modest contribution to the application of these old dual debaters.