Here s(X) denotes the total number of fragments rooted at base symbol X. for fragments f in G by where now b , r and e are non-indexed type abstractions of f 's member productions in G I and Under the weight function ω G (f ), any derivation d in G will have weight which obeys and so the posterior P (d|s) of a derivation d for a sentence s will be the same whether computed in G or G I .
provided our weighting function on fragments f in G decomposes over the derivational representation of f in G I , we can equivalently compute the quantities we need for inference (see Section 4) using G I instead.