The category game models the communication protocols between two agents who aim to match category labels with elements encountered in a simulated ()r real world. In the language games community the expressions available to an agent has traditionally centered on category label assertions. This thesis presents a new representation for category labels, in which category definitions explicitly Incorporate semantic uncertainty and typicality. More specifically, a conceptual model based on prototype and random set theory is proposed, in which categories are defined within a metric conceptual space. It is argued that this conceptual framework is both expressive and naturally generates robust assertion and concept updating models. This is demonstrated by the development of assertion and updating rules which allow compound logical expressions of category labels to be used in agent interaction. In particular, in multi-agent simulations of the category game under this framework, agents use a mixture of category labels and negated labels. The results of these simulations are presented, where a multi-agent system evolves through pairwise language games, implementing several different assertion and updating algorithms. The performance is measured in terms of the average distance between agents' conceptual interpretations, and results suggest that, within this framework, a mixture of both positive and negative assertions are required in order for the multi-agent systems to evolve so that agents share sufficiently similar interpretations covering the space, which are also able to discriminate between different cases. These results are supported in subsequent chapters where two further language games are implemented, suggesting that using a mixture of assertions shows the best possible communication success between agents. An investigation into the role of feedback in the category game compares simulations in which agents use feedback with the results of simulations without feedback. All results presented suggest that using feedback allows agents to develop a set of interpretations which are more similar than if feedback was not being implemented, and also allows agents to obtain a higher value for average communication success. Finally, we introduce a bipolar mode~ of assertion. This allows agents to make an assertion with two degrees of celtainty, and may be used as a strategy to gain higher reward and lower punishment in a category game implementing a feedback model.