  We investigate the competition between different orders in the two-leg spin
ladder with a ring-exchange interaction by means of a bosonic approach. The
latter is defined in terms of spin-1 hardcore bosons which treat the N\'eel and
vector chirality order parameters on an equal footing. A semiclassical approach
of the resulting model describes the phases of the two-leg spin ladder with a
ring-exchange. In particular, we derive the low-energy effective actions which
govern the physical properties of the rung-singlet and dominant vector
chirality phases. As a by-product of our approach, we reveal the mutual
induction phenomenon between spin and chirality with, for instance, the
emergence of a vector-chirality phase from the application of a magnetic field
in bilayer systems coupled by four-spin exchange interactions.
