  In this paper we discuss the consistency concept of Williams coherence for
imprecise conditional previsions, presenting a variant of this notion, which we
call W-coherence. It is shown that W-coherence ensures important consistency
properties and is quite general and well-grounded. This is done comparing it
with alternative or anyway similar known and less known consistency
definitions. The common root of these concepts is that they variously extend to
imprecision the subjective probability approach championed by de Finetti. The
analysis in the paper is also helpful in better clarifying several little
investigated aspects of these notions.
