Since polysemy has multiple but related senses, finding any coherent system would seem impossible. But its senses are not random. When we look at inferences among them, it becomes clear that there must be a systematic structure of some kind. Based on the prototype theory, which views lexical items as constituting natural categories of senses, the present work aims at proposing solutions to problems resulting from the polysemy of kai. After an in-depth analysis of the polysemy kai, we find that the links between polysemy senses are defined not only by shared properties (i.e. analogy), but also by conceptual connections (e.g. metonymy or metaphor). This study suggests that polysemy reflects human``s categorization of things and can be successfully accounted for by a cognitive approach.