The semilattice relevant logics UR, UT, URW, and UTW (slightly different 
from the orthodox relevant logics R, T, RW, and TW) are defined by 
``semilattice models'' in which conjunction and disjunction are interpreted 
in a natural way. In this paper, we prove the equivalence between ``LK-style''
and ``LJ-style'' labelled sequent calculi for these logics. (LK-style sequents
have plural succedents, while they are singletons in LJ-style.) Moreover, 
using this equivalence, we give the following. (1) New Hilbert-style 
axiomatizations for UR and UT.  (2) Equivalence between two semantics 
(commutative monoid model and distributive semilattice model) for the 
``contractionless'' logics URW and UTW.