  For a partial lattice L the so-called two-point extension is defined in order
to extend L to a lattice. We are motivated by the fact that the one-point
extension broadly used for partial algebras does not work in this case, i.e.
the one-point extension of a partial lattice need not be a lattice. We describe
these two-point extensions and prove several properties of them. We introduce
the concept of a congruence on a partial lattice and show its relationship to
the notion of a homomorphism and its connections with congruences on the
corresponding two-point extension. In particular we prove that the quotient L/E
of a partial lattice L by a congruence E on L is again a partial lattice and
that the two-point extension of L/E is isomorphic to the quotient lattice of
the two-point extension L* of L by the congruence on L* generated by E. Several
illustrative examples are enclosed.
