In a series of papers Kubota and Levine give an account of gapping and determiner gapping in terms of hybrid type logical grammar, including anomalous scopal interactions with auxiliaries and negative quantifiers. We make three observations: i) under the counterpart assumptions that Kubota and Levine make, the existent displacement type logical grammar account of gapping already accounts for the scopal interactions, ii) Kubota and Levine overgenerate determiner-verb order permutations in determiner gapping conjuncts whereas the immediate adaptation of their proposal to displacement type logical grammar does not do so, and iii) Kubota and Levine do not capture simplex gapping as a special case of complex gapping, but require distinct lexical entries for the two cases; we show how a generalisation of displacement type logical grammar allows both simplex and discontinuous gapping under a single type assignment