Towards a mathematical theory of meaningful communication

TL;DR

This paper proposes a mathematical framework to incorporate meaning into information theory, addressing limitations of traditional probabilistic models and demonstrating how meaningful communication can be properly quantified and understood.

Contribution

It introduces a new theoretical approach inspired by Saussure's duality of signs to measure meaningful information in communication systems.

Findings

Traditional models can lead to paradoxes like maximum information with wrong interpretations

The proposed framework accurately captures the minimal system for meaningful information decoding

Some transmitted information may be useless for effective communication among autonomous agents

Abstract

Despite its obvious relevance, meaning has been outside most theoretical approaches to information in biology. As a consequence, functional responses based on an appropriate interpretation of signals has been replaced by a probabilistic description of correlations between emitted and received symbols. This assumption leads to potential paradoxes, such as the presence of a maximum information associated to a channel that would actually create completely wrong interpretations of the signals. Game-theoretic models of language evolution use this view of Shannon's theory, but other approaches considering embodied communicating agents show that the correct (meaningful) match resulting from agent-agent exchanges is always achieved and natural systems obviously solve the problem correctly. How can Shannon's theory be expanded in such a way that meaning -at least, in its minimal referential form- is properly incorporated? Inspired by the concept of {\em duality of the communicative sign} stated by the swiss linguist Ferdinand de Saussure, here we present a complete description of the minimal system necessary to measure the amount of information that is consistently decoded. Several consequences of our developments are investigated, such the uselessness of an amount of information properly transmitted for communication among autonomous agents.