Our models follow a standard generative story for head-outward automata (Alshawi, 1996a), restricted to the split-head case (see below), 1 over lexical word classes {cw}: first, a sentence root cr is chosen, with probability PATTACH(cr | ⋄; L); ⋄ is a special start symbol that, by convention (Klein and Manning, 2004;Eisner, 1996), produces exactly one child, to its left.
we presuppose that all sentences are assigned to one of two classes: complete and incomplete (comp ∈ {T, F}, for now taken as exogenous).