In CFG we "simply" have production rules. Whereas in Combinatory Categorial Grammar (CCG) on the other hand, we have both composition rules over categories, and a mapping from syntax to semantics (from the categories to lambda expressions).
Could we equivalently use such mappings to semantics, over a CFG framework, to obtain semantic representations? similarly to how we use such mappings in CCG? asked differently and perhaps more precisely, what would a combinatory formalism for semantics over CFG look like? would it just in fact be CCG, or would the production rules play any role?