A p-adic probability logic

Abstract

In this article we present a p-adic valued probabilistic logic which is a complete and decidable extension of classical propositional logic. The key feature of lies in ability to formally express boundaries of probability values of classical formulas in the field of p-adic numbers via classical connectives and modal-like operators of the form K r, ρ. Namely, is designed in such a way that the elementary probability sentences K r, ρα actually do have their intended meaning-the probability of propositional formula α is in the -ball with the center r and the radius ρ. Due to modal nature of the operators K r, ρ, it was natural to use the probability Kripke like models as structures, provided that probability functions range over instead of or.