 It is natural to ask after a syntactical condition related to pseudo-truth-functionality in the same way(s) as full determination is related to truth-functionality. Say that an n-ary connective # is left-extensional in its ith position (1 ≤ i ≤ n) or right-extensional in its ith position, according to a generalized consequence relation ⊩, when the condition (LEi) or (REi) is satisfied, respectively, for all formulas φ1,…,φn,ψ in the language of ⊩ we have: