A p-adic probability logic
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 Kr, ?. Namely, is designed in such a way that the elementary probability sentences Kr, ?? actually do have their intended meaningthe probability of propositional formula ? is in the -ball with the center r and the radius ?. Due to modal nature of the operators Kr, ?, it was natural to use the probability Kripke like models as -structures, provided that probability functions range over instead of or .
probability logic p-adic numbers. [msc2010]03b48 68t27