Bayesian probability theory is clearly the sought mathematical alternative to logic.
However, we want working solutions to incomplete and uncertain problems. Consequently, we require an alternative computing framework based on Bayesian probabilities.
To create such a complete computing Bayesian framework, we reqire a new modeling methodology to build probabilistic models, we require new inference algorithms to automate probabilistic calculus, we require new programming languages to implement these models on computers, and finally, we will eventually require new hardware to run these Bayesian programs efficiently.
The ultimate goal is a Bayesian computer. One of the two main purposes of our research group is to advance in this direction.