Language games with vague categories and negations

Language games model the communication protocols between two agents who aim to match category labels with objects encountered in a simulated or real environment. Here we present a new representation framework for such games, in which category definitions explicitly incorporate semantic uncertainty and typicality. More specifically, we propose a conceptual model based on prototype and random set theory, in which categories are defined within a metric conceptual space. We argue that this conceptual framework is both expressive and naturally generates robust assertion and concept updating models. In particular, we define both assertion and updating rules for language games involving a mixture of labels and negated labels. Finally, the results of language game simulations are presented, where a multi-agent system evolves through pairwise language games incorporating an assertion and an updating algorithm. Our results suggest that, within this framework, a mixture of both positive and negative assertions may be required in order for agent interpretations to converge, whilst retaining sufficiently discriminatory categories for effective communication.