The question how a shared vocabulary can arise in a multi-agent population despite the fact that each agent autonomously invents and acquires words has been solved. The solution is based on alignment: Agents score all associations between words and meanings in their lexicons and update these preference scores based on communicative success. A positive feedback loop between success and use thus arises which causes the spontaneous self-organization of a shared lexicon. The same approach has been proposed for explaining how a population can arrive at a shared grammar, in which we get the same problem of variation because each agent invents and acquires their own grammatical constructions. However, a problem arises if constructions reuse parts that can also exist on their own. This happens particularly when frequent usage patterns, which are based on compositional rules, are stored as such. The problem is how to maintain systematicity. This paper identifies this problem and proposes a solution in the form of multilevel alignment. Multilevel alignment means that the updating of preference scores is not restricted to the constructions that were used in the utterance but also downward and upward in the subsumption hierarchy.
