| Abstract: | Formal dialogue games studied by philosophers since the time of Aristotle have recently found application in Artificial Intelligence as the basis for protocols for interactions between autonomous software agents. For instance, game protocols have been proposed for agent dialogues involving team formation, persuasion, negotiation and deliberation. There is yet, however, no formal, mathematical theory of dialogue game protocols with which to compare two protocols or to study their formal properties. In this paper,1 we present preliminary work towards such a theory, in which we develop a geometric semantics for these protocols and, with it, define a notion of equivalence between two protocols. We then demonstrate an algebraic property of protocol equivalence, and use this to show the non-equivalence of two similar generic protocols. We also explore the relationship between finite and infinite dialogues, motivated by the Ehrenfeucht-Fraïssé games of model theory. Our results have implications for the design and evaluation of agent dialogue-game protocols. |
