  In this paper, we study proof systems in the sense of Cook-Reckhow for
problems that are higher in the polynomial hierarchy than coNP, in particular,
#SAT and maxSAT. We start by explaining how the notion of Cook-Reckhow proof
systems can be apply to these problems and show how one can twist existing
languages in knowledge compilation such as decision DNNF so that they can be
seen as proof systems for problems such as #SAT and maxSAT.
