A depth-first search algorithm for computing pseudo-closed sets

The question of the lower bounds for the delay in the computation of the Duquenne-Guigues implication basis in non-lectic orders is still open. As a step towards an answer, we propose an algorithm that can enumerate pseudo-closed sets in orders that do not necessarily extend the inclusion order using depth-first searches in a sequence of closure systems. Empirical comparisons with NextClosure on the runtime and number of closed sets computed are provided.