Introduction

Abstract

One of the most important problems initiated by quantum theory is a mathematical description of the structure of random events of a quantum mechanical system. This problem was originally formulated in the famous paper by G. Birkhoff and J. von Neumann “The Logic of Quantum Mechanics” in 1936. The fundamental difficulty is the existence of quantum phenomena that cannot be described in terms of the event structure of the classical Kolmogorovian probability theory. It is noteworthy that similar situations seem to arise in other areas of sciences; e.g., psychology, design of computers, neural networks, and the biology of the human brain.