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This article contains a proposal to add coinduction to the computationalapparatus of natural language understanding. This, we argue, will provide abasis for more realistic, computationally sound, and scalable models of naturallanguage dialogue, syntax and semantics. Given that the bottom up, inductivelyconstructed, semantic and syntactic structures are brittle, and seeminglyincapable of adequately representing the meaning of longer sentences orrealistic dialogues, natural language understanding is in need of a newfoundation. Coinduction, which uses top down constraints, has been successfullyused in the design of operating systems and programming languages. Moreover,implicitly it has been present in text mining, machine translation, and in someattempts to model intensionality and modalities, which provides evidence thatit works. This article shows high level formalizations of some of such uses.  Since coinduction and induction can coexist, they can provide a commonlanguage and a conceptual model for research in natural language understanding.In particular, such an opportunity seems to be emerging in research oncompositionality. This article shows several examples of the joint appearanceof induction and coinduction in natural language processing. We argue that theknown individual limitations of induction and coinduction can be overcome inempirical settings by a combination of the the two methods. We see an openproblem in providing a theory of their joint use.

Towards Coinductive Models for Natural Language Understanding. Bringing together Deep Learning and Deep Semantics