A Category Theory of Communication Theory
This provides a theoretical framework for language understanding in AI, but it is incremental as it builds on existing mathematical formalisms without empirical validation.
The paper tackles the problem of how agents can understand language by formalizing it as associating operators with sentences that transform the agent's representational state, using category theory concepts and diagrams.
A theory of how agents can come to understand a language is presented. If understanding a sentence $α$ is to associate an operator with $α$ that transforms the representational state of the agent as intended by the sender, then coming to know a language involves coming to know the operators that correspond to the meaning of any sentence. This involves a higher order operator that operates on the possible transformations that operate on the representational capacity of the agent. We formalize these constructs using concepts and diagrams analogous to category theory.