Concepts and Types - An Application to Formal Language Theory

We investigate how formal concept analysis can be applied in a type-theoretic context, namely the context of λ-terms typed à la Curry. We first show some general results, which reveal that concept lattices generally respect and reflect the type structure of terms. Then, we show an application of the results in formal language theory, where we vastly generalize existing approaches of capturing the distributional structure of languages by means of formal concept analysis. So type theory is interesting to formal concept analysis not only as a particular context, but also because it allows to generalize existing contexts.