  A sectionally pseudocomplemented poset P is one which has the top element and
in which every principal order filter is a pseudocomplemented poset. The
sectional pseudocomplements give rise to an implication-like operation on P
which coincides with the relative pseudocomplementation if P is relatively
psudocomplemented. We characterise this operation and study some elementary
properties of upper semilattices, lower semilattices and lattices equipped with
this kind of implication. We deal also with a few weaker versions of
implication. Sectionally pseudocomplemented lattices have already been studied
in the literature.
