  In order to be able to use methods of Universal Algebra for investigating
posets, we assign to every pseudocomplemented poset, to every relatively
pseudocomplemented poset and to every sectionally pseudocomplemented poset a
certain algebra (based on a commutative directoid or on a lambda-lattice) which
satisfies certain identities and implications. We show that the assigned
algebras fully characterize the given corresponding posets. It turns out that
the assigned algebras satisfy strong congruence properties which can be
transferred back to the posets. We also mention applications of such posets in
certain non-classical logics.
