Re: quantum logic

I will let others answer about the connection between closed monoidal categories and MLL, but I just wanted to say that I am not sure what you mean by the category of Hilbert spaces. If you want the inner product preserved, then only isometric injections are permitted. If you want just bounded linear maps then you are not making any real use of the inner product. And the spaces are self-dual, so it is not a good model of *-autonomy. Perhaps of compact categories, I would have to think about it. But anyway, you have to say what category is meant. Another possibility is partial isometries (which can be thought of as total by being zero on the subspace orthognal to the domain). This is a lot like sets and partial injections. Michael