Some considerations regarding mathematical semiosis

The discussion on the possibility of machines to achieve semiosis (meaning process) is a very controversial debate within Artificial Intelligence and Cognitive Science. In this work, we define meaning process in an entirely mathematical framework. We call the "transposition" of the Peircean theory to an abstract mathematical model as "Mathematical Semiosis". By doing this, we aim at growing a more understandable theory for explaining what is to mean, in a strictly mathematical sense, avoiding complications related to the connection of signs to a real world. The main application of such a theory would be in order to develop machines with these capabilities. In such a regard, what we are calling here "Mathematical Semiosis" would be a kind of purely mathematical abstraction for what is "Semiosis" in the real world.