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.