Practical reasoning is the process of drawing conclusions relative to evidence, goals, and risks. We present a computational model of dialectical argumentation as basis for practical reasoning in weak-theory domains, i.e., incomplete, uncertain, and inconsistent contexts. As information structure, an argument consists of argument units connecting claims with supporting data. As dialectical process, an argument consists of an alternating series of moves by opposing sides. Burden of proof, i.e., which side of an argument must realize what level of support. acts as move filter and termination criterion. Other aspects of our model include: (i) arguments defeat other arguments, not claims; (ii) not all conflicting arguments are defeating arguments; and (iii) whether a claim is believed or not depends in part upon the burden of proof specified.