Non-Conventional Probability Theories, their importance and applications

Abstract

The concept of probability has fascinated scientists and philosophers for a long time, dating back to Blaise Pascal's solution to gaming problems in1654. Initially seen as a tool to deal with uncertainty, probability has evolved into a fundamental measure of randomness, impacting fields from genetics to quantum mechanics. Despite its widespread application, interpretations of probability remain controversial, sparking debates in the philosophy of science. Philosophers like Carnap and Popper explored its connection withlogic, proposing different interpretation. Meanwhile, independent from such debates, paraconsistent logics have emerged as a method to address the role of contradictions in rationality. Recent research combines probability, paraconsistency abd paracompleteness, aiming to redefine Kolmogorov's theory and refine Popper's concepts. The present project extends into two fronts:1) Refining the Logic of Evidence and Truth,exploring new algebraic methods regarding probability theory.2) Investigating trivalent paraconsistent logics as a fondation for a new theory of probability. A recent trivalent approach validates Stalnaker's thesis, showing potential to overcome bivalent limitations and trivial results. These advancements, combined with the Logics of Formal Inconsistency, offer promising avenues for the development of innovative probability theories.