Towards p-adic artificial language

Abstract

Motivated by successful p-adic modeling of the genetic code, in this paper a p-adic (ultrametric) language is introduced. This language can serve as an effective and advanced constructive element of a future artificial intelligence. In this geometric approach to artificial language, we mainly use p-adic distance as the most powerful example of ultrametrics. Here p-adic distance is a tool to quantify similarity between words - similarity between their structure and similarity between their meaning. As a simple illustration, a p-adic language with four letters and their 3-letter words is presented.