A mathematical model of interactions in artifact environments

We always interact with our environment in our life. When we use artifacts, we interact with the environment through them, or rather, we interact with the artifacts as our environment. When we design and manufacture artifacts, it is important to consider the interaction. In this paper, we propose a mathematical model of interactions by focusing on the role or the function of interfaces. Our modeling consists of three steps. Firstly, we propose a new view about the role of an interface in a interaction. Then, we formulate the function of an interface by using the idea of Situation Semantics, a formal semantics of natural languages by Bitwise and Perry. At last, we give a mathematical model of interactions based on Channel Theory, a mathematical theory of information flow by Bitwise and Seligman. An example of a case of an interaction between a human and an environment through an artificial neural network is be presented.