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?

  • 2
    It's possible but less straightforward. Instead of applying lambda calculus one usually just combines formulae using conjunction and the CF rules control the unification of variables. Before parsing, you'd have, say, see(x,y), girl(u) and dog(v) (from the lexicon), and in the course of parsing one unifies x with u and y with v, thus yielding the logical form of the sentence.
    – Atamiri
    Feb 17, 2017 at 21:04

1 Answer 1


If you can get from CG (Categorial Grammar) to the semantic mappings you want, I can show you a way to get from CFG (Context Free Phrase Structure Grammar) to CG. So the answer to your question might possibly be "yes", since CFG => CG and CG => CCG would imply (I guess) that CFG => CCG.

I gave a brief account of how to get from my theory, "2psg", which is an elaboration of PSG, to CG, in answer to a previous question on this forum, here: my second answer to question about particles. The basic idea is to reformulate the information given in a node of a CG structure diagram as a phrase structure rule.

A basic problem in going from CFG to CG is that when phrase structure rules are combined to derive a new phrase structure rule, the derivation is not naturally functional, whereas the corresponding operation in CG is a function. I've described a way to force the derivation of a phrase structure rule from others into functional form by making use of some ideas from Relational Grammar. See my post on 2psg.

Referring to Wikipedia on CCG, I can reconstruct "application combinators" and a special case of "composition combinators".

  • You'd need to show CCG => CFG to answer in the positive, which would possibly mean CfG <=> CCG.
    – vectory
    May 19, 2020 at 9:44

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