In this paper, we present a computational model of dialectical argumentation. As a structure of supports and rebuttals, an argument consists of a series of qualified claims and their backings. When viewed as a process of interacting moves, an argument consists of move generation functions and selection heuristics. We introduce a concept of burden of proof which acts as filter on applicable moves and as termination criterion, determining when an argument has been completed and which side has won. Burden of proof is an important component of argumentation when used as a means for making decisions in the context of uncertain, incomplete, and conflicting knowledge.