Modelling Multi-agent Interaction Protocols Using Categories Enriched over Pointed Sets

The study of multi-agent systems is proving to be an exciting and active research field within computer science. Communication is an important aspect of multi-agent systems, and the protocols that are used to provide a shared definition of what agents can say to each other, along with the meaning of what agents say, receive much attention from researchers. At present, there are a number of well-defined protocols, agent communication languages, and protocol specification languages available, yet, there is no formal mathematical theory of agent interaction protocols. The authors believe that such a theory would be beneficial to the field of agent communication and multi-agent systems in general. In this paper, we present an application of the mature field of category theory for modelling interaction protocols. Using category theory, specifically, a subsidiary theory of category theory known as enriched category theory, we demonstrate how to model the legal utterances of a protocol, and to assign the meaning of utterances, such as commitments to perform a certain action. Enriched categories obey the rules of categories, so we argue that using them to model protocols gives us a mature theory for modelling and reasoning about protocols, and the relationships between them.