Ample Probability in Cognition

Abstract

This paper assumes probability is a bridge linking cognition and computing. We begin with the dynamic and causal structuring of random events and represent them 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. The proposed axioms are consistent and independent giving in the limit Kolmogorov's axiom system for conventional probability. In addition, we comment on the relations between ample probability, conditional probability and quantum probability.