Basic Concepts of the Theory of Ample Probability
Mark Burgin1*, Paolo Rocchi2
1*University of California, Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095, USA.
2Libera Universita Internazionale degli Studi Sociali Guido Carli, Rome, Italy and IBM Italia, Rome, Italy.
Employing dynamic or causal structuring of events and their representation in the form of named sets, we construct a probability function called ample probability for such events and develop elements of an axiomatic ample probability theory. We show (Theorem 4.2) that axioms that characterize ample probability are consistent and independent. It is also proved that in the limit, i.e., when all named sets representing events are single named sets, the axiom system for ample probability becomes Kolmogorov’s axiom system for conventional probability (Theorem 4.1). Using the introduced axiomatic system of ample probability, we study properties of ample probability. In addition, we show how ample probability works by means of structuration of events for calculating their probabilities.
Key words: Probability, Axiom, Transition, Independence, Consistency.