MARCO ANTONIO ANTONELLI GAIARSA

This research aims to examine the fundamental elements of Decision Theory. A first chapter is dedicated to introducing the situations and problems that lead to the fundamental questions of this area. In this chapter, intuitions are refined and formalized until it is possible to examine the general outlines of the Bayesian solution, called, in the context of this work, classical theory. The following two chapters are dedicated to examining and deepening the two key terms: belief and preference. The second chapter deals with belief, examining inductive logic, subjective probability and the challenges of traditional approaches. The third chapter looks at preference, examining the justifications for the conditions imposed by the classical approach and reflecting on their validity. The axiom of completeness is challenged more vigorously, pointing out paradoxes and paths of solution.