A theory of interaction semantics

The aim of this article is to delineate a theory of interaction semantics and thereby provide a proper understanding of the "meaning" of the exchanged characters within an interaction. The key idea is to approach the semantics of an interaction as we do for a formal language. This approach consists of two steps: first to assign values to variables and second to provide meaning by an interpretation function. A natural choice for the variables are the state functions of the interacting systems, assigning values at each time step. Thereby the description of a system's behaviour with an input/output-transition system (I/O-TS) becomes a representation of the variable-to-value assignments.To identify the interpretation function I propose to model the interaction of systems based on Shannon's theory of information with the protocol concept, complemented by decisions to form a "game in interactive form (GIF)". Decisions in this sense determine the transition relation and thereby create a transition function. Then the natural choice for the interpretation function is the transition function of the GIF. In this sense, the interpretation of the interaction becomes its execution. Now we can say that the interpretation of the characters during the GIF's execution results in their meaning, the result of the mapping. Equivalent meaning is based on resulting equivalent states of the GIF. Based on the decisions we can partition any GIF into a deterministic traditional automaton where the states represent equivalance classes of GIF-states related to a single decision. Except for the utility function, this automaton is equivalent to a traditional game in extensive form. Thus, traditional game theory actually abstracts from interactions and deals with the meaning of decisions.