We explore the use of argumentation for justifying claims reached by plausible reasoning methods in domains where knowledge is incomplete, uncertain, or inconsistent. We present elements of a formal theory of argumentation that includes two senses of argument, argument as supporting explanation and argument as dialectical process. We describe a partial implementation of the theory, a program that generates argument structures that organize relevant, available, plausible support for both a claim and its negation. Then we describe a theory of argument as dialectical process, where the format of a two-sided argument is used to intertwine the strengths and weaknesses of support for competing claims, so arguments can be refuted and directly compared.