Learning the Semantics of Notational Systems with a Semiotic Cognitive Automaton

Abstract

Through semiotic modelling, a system can retrieve and manipulate its own representational formats to interpret a series of observations; this is in contrast to information processing approaches that require representational formats to be specified beforehand and thus limit the semantic properties that the system can experience. Our semiotic cognitive automaton is driven only by the observations it makes and therefore operates based on grounded symbols. A best-case scenario for our automaton involves observations that are univocally interpreted—i.e. distinct observation symbols—and that make reference to a reality characterised by “hard constraints”. Arithmetic offers such a scenario. The gap between syntax and semantics is also subtle in the case of calculations. Our automaton starts without any a priori knowledge of mathematical formalisms and not only learns the syntactical rules by which arithmetic operations are solved but also reveals the true meaning of numbers by means of second-order reasoning.