I can see ways to represent lambda calculus constructs using CT and viceversa. I guess that 'systems of logic' includes lambda calculus, or systems with equivalent semantics; so yeah, I can believe there's a connection at some level.
The (one?) problem with CT is that it, by definition, puts too much importance on the relation between things via composition, which is a powerful paradigm in itself, but also quite restrictive. 'Structure' is not usually encoded like that in a natural way.
CT is just part of a larger framework that is currently being unveiled (!!!); but, to be quite frank, people who focus mostly on CT seem to be missing the forest for the trees.
The (one?) problem with CT is that it, by definition, puts too much importance on the relation between things via composition, which is a powerful paradigm in itself, but also quite restrictive. 'Structure' is not usually encoded like that in a natural way.
CT is just part of a larger framework that is currently being unveiled (!!!); but, to be quite frank, people who focus mostly on CT seem to be missing the forest for the trees.