A Mathematical Model of Dialog

Computer Science is currently undergoing a paradigm shift, from viewing computer systems as isolated programs to viewing them as dynamic multi-agent societies. Evidence of this shift is the significant effort devoted recently to the design and implementation of languages and protocols for communications and interaction between software agents. Despite this effort, no formal mathematical theory of agent interaction languages and protocols yet exists. We argue that such a theory needs to account for the semantics of agent interaction, and propose the first mathematical theory which does this. Our framework incorporates category-theoretic entities for the utterances made in an agent dialog and for the commitments incurred by those utterances, together with maps between these.