Mathematical linguistics and cognitive complexity

The complexity of linguistic patterns has been object of extensive debate in research programs focused on probing the inherent structure of human language abilities. But in what sense is a linguistic phenomenon more complex than another, and what can complexity tell us about the connection between linguistic typology and human cognition? This chapter approaches these questions by presenting a broad and informal introduction to the vast literature on formal language theory, computational learning theory, and artificial grammar learning. In doing so, it hopes to provide readers with an understanding of the relevance of mathematically grounded approaches to cognitive investigations into linguistic complexity, and thus further fruitful collaborations between cognitive scientists and mathematically inclined linguist and psychologist.