On Evolution of Compositionality Sanne Brinkhorst Abstract: This thesis focusses on the question how compositional language emerged. Two new models for combinatorial message use are presented. In these models two agents play a Lewis signalling game. The first model is an adaptation of the Barrett-Skyrms model for multiple messages. This adaptation allows for message of arbitrary length and is less likely to get caught in a pooling equilibrium than existing models do. The second model is an artificial neural network approach. In this model it is more likely that a signalling strategy with perfect information transfer emerges and the agents can communicate about states that are not trained but are similar to the states that are known. Keywords: logic, language