Chris Barker just posted a nice paper setting out some features of type-logical grammar to the Semantics Archive. I don’t know enough about syntax to be able to compare type-logical approaches to categorial grammars, let alone more orthodox GB-style approaches. But I was very interested to see the way substructural logics are being used here. If I was trying to find a theory of grammaticality, I would not have thought to approach it by analogy to validity in a weak linear logic, but that’s just what some theorists have done, with impressive results.

One of the things I often say when defending abstract philosophical work is that it can have benefits down the track that seem completely unrelated to its initial motivation. While I think some of the early researchers on weak substructural logics were motivated by concerns about syntax, this doesn’t seem to have been a widespread motivation. I don’t think Gentzen, for instance, saw his work on formalising the sequent calculus as being particularly related to the project of unifying natural language syntax and semantics, but that’s one of the ways it is being used now. The Law of Unintended Consequences often leads to very pleasant outcomes in philosophy.