What are the unique design features of language? Formal tools for comparative claims

What are the "design features" of human language that need to be explained? Starting from R. Jackendoff's scenario for the evolution of language, we argue that it is the transitions between stages that pose the crucial challenges for accounts of the evolution of language. We review a number of formalisms for conceptualizations, sound, and the mapping between them, and describe and evaluate the differences between each of Jackendoff's stages in terms of these formalisms. We conclude from this discussion that the transitions to combinatorial phonology, compositional semantics and hierarchical phrase structure can be formally characterized. Modeling these transitions is a major challenge for language evolution research.