Furthermore, in a TT-MCTAG derivation the argument trees must either adjoin directly to their head tree, or they must be linked in the derivation tree to an elementary tree that attaches to the head tree, by means of a chain of adjunctions at root nodes.
items have the form [γ, p t , i, f 1 , f 2 , j] where γ ∈ i ∪ A, p is the address of a node in γ, subscript t ∈ {⊤, ⊥} specifies whether substitution or adjunction has already taken place (⊤) or not (⊥) at p, and 0 ≤ i ≤ f 1 ≤ f 2 ≤ j ≤ n are indices with i, j indicating the left and right edges of the span recognized by p and f 1 , f 2 indicating the span of a gap in case a foot node is dominated by p. We write f 1 = f 2 = − if no gap is involved.