1 To flatten the notation, we will generally represent items as a 4-tuple, e.g.
in CKY, new items are created by applying rules to existing items: (5) we are allowed to apply a rule r to a pair of items ι 1 , ι 2 if the item spans are complementary and preconditions(r) = postcondition(ι 1 ), postcondition(ι 2 ) .