  This paper explores the conditions under which modified gravitational
theories admit the positive mass. Following Witten's spinor argument, it is
argued that a single condition should be imposed upon a gauge connection in the
super-covariant derivative. Under this condition, we present a simple formula
for the divergence of the Nester tensor in Einstein's gravity with general
source. Applying this prescription to the Einstein-scalar system, we find that
for a certain class of the gauge connection, a special kind of non-canonical
scalar-field theory admits the positivity property in addition to the ordinary
canonical scalar-field system. In both cases the scalar potential can be
written in terms of a superpotential. In the non-canonical case we obtain the
most general "BPS" solutions which preserve at least half of the supersymmetry.
