A Category Theory of Communication Theory

TL;DR

This paper develops a formal framework using category theory to model how agents learn and understand language through operators that transform their representational states, involving higher-order transformations.

Contribution

It introduces a novel categorical formalization of language understanding, emphasizing higher-order operators and their role in learning language meanings.

Findings

Formalizes language understanding using category theory concepts.

Defines higher-order operators for modeling language acquisition.

Provides a diagrammatic approach to represent transformations in understanding.

Abstract

A theory of how agents can come to understand a language is presented. If understanding a sentence $\alpha$ is to associate an operator with $\alpha$ that transforms the representational state of the agent as intended by the sender, then coming to know a language involves coming to know the operators that correspond to the meaning of any sentence. This involves a higher order operator that operates on the possible transformations that operate on the representational capacity of the agent. We formalize these constructs using concepts and diagrams analogous to category theory.