Embodied cognition, language, and mirror neuron system

Language and cognition seems to be very different, they are studied in different university departments, they are located in different parts of the brain, still nature gives us no separate examples of these abilities. What exactly is similar and different among language and cognition? What are functions of language in cognition, and vice versa? How are these abilities embodied? The paper develops mathematical model of interacting cognition and language based on existing cognitive data and closely related to mirror neuron system. Dynamic logic modeling fundamental mechanisms of the mind leads to a hypothesis answering above questions. Future research and verifiable experimental predictions are discussed.