Interestingly, one can show that in the propositional case, this prediction is equivalent toφ(d)⇔ φ(>), i.e. we only need to consider one possible sentence completion β: the tautology. Importantly however, this is only a (very efficient) technical shortcut and lengthy tautologous pieces are not necessary (see Chemla, 2006). This first part of the theory accounts for the core projection facts: p...