Mathematical Model of Meaning

Meaning is not attributed to the message itself but rather emerges from its action on the recipient. On this principal idea a mathematical model of meaning can be constructed. The recipient is defined by a set of its states; the message is an operator that acts on these states and transfers the recipient from one state into another. Meaning should be ascribed to neither the recipient state nor the message operator; meaning emerges while the set of recipient states maps to itself and the recipient transfers from one state to another by the message operator. This general approach can be realized in terms of such formalisms as automata theory, matrix representation, algorithms, Markov chains, parameter space, and others. Different classes of meanings are considered including finite, countable, and continuous; reversible and irreversible; deterministic and probabilistic ones. It is shown that an arbitrary meaning operator can be decomposed in to a product of elementary meaning operators in case of their associativity.