  We prove that every not necessarily bounded poset P=(P,\le,') with an
antitone involution can be extended to a residuated poset
E(P)=(E(P),\le,\odot,\rightarrow,1) where x'=x\rightarrow0 for all x\in P. If P
is a lattice with an antitone involution then E(P) is a lattice, too. We show
that a poset can be extended to a residuated poset by means of a finite chain
and that a Boolean algebra (B,\vee,\wedge,',p,q) can be extended to a
residuated lattice (Q,\vee,\wedge,\odot,\rightarrow,1) by means of a finite
chain in such a way that x\odot y=x\wedge y and x\rightarrow y=x'\vee y for all
x,y\in B.
