Towards a mathematical theory of meaningful communication
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 As a consequence, functional responses based on an appropriate interpretation of signals has been replaced by a probabilistic description of correlations between emitted and received symbols.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. Gametheoretic 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 agentagent 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2010
 arXiv:
 arXiv:1004.1999
 Bibcode:
 2010arXiv1004.1999C
 Keywords:

 Computer Science  Information Theory;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems;
 Quantitative Biology  Other Quantitative Biology
 EPrint:
 10 RevTex pages, 3 figure