  The arrival of Immersive Virtual and Augmented Reality hardware to the
consumer market suggests seamless multi-modal communication between human
participants and autonomous interactive characters is an achievable goal in the
near future. This possibility is further reinforced by the rapid improvements
in the automated analysis of speech, facial expressions and body language, as
well as improvements in character animation and speech synthesis techniques.
However, we do not have a formal theory that allows us to compare, on one side,
interactive social scenarios among human users and autonomous virtual
characters and, on the other side, pragmatic inference mechanisms as they occur
in non-mediated communication.
  Grices' and Sperbers' model of inferential communication does explain the
nature of everyday communication through cognitive mechanisms that support
spontaneous inferences performed in pragmatic communication. However, such a
theory is not based on a mathematical framework with a precision comparable to
classical information theory.
  To address this gap, in this article we introduce a Mathematical Theory of
Inferential Communication (MaTIC). MaTIC formalises some assumptions of
inferential communication, it explores its theoretical consequences and
outlines the practical steps needed to use it in different application
scenarios.
