Non-Well-Founded Probabilities and Coinductive Probability Logic

One of the most useful computer algebra used today is calgebra and its versions, e.g. stream calculus. In the paper I show that p-adic arithmetic can be regarded as one of the natural interpretation of stream calculus on a finite set of positive integers. Further, I define probabilities on streams using bisimulation and construct probability logic with non-well-founded syntax and non-well-founded semantics.