The Logic of Multiple-Valued Argumentation (LMA) is an argumentation framework that allows for argument-based reasoning about uncertain issues under uncertain knowledge. In this paper, we describe its applications to Social Web: SNS and Wikipedia. They are said to be the most influential social Web applications to the present and future information society. For SNS, we present an agent that judges the registration approval for Mymixi in mixi in terms of LMA. For Wikipedia, we focus on the deletion problem of Wikipedia and present agents that argue about the issue on whether contributed articles should be deleted or not, analyzing arguments proposed for deletion in terms of LMA. These attempts reveal that LMA can deal with not only potential applications but also practical ones such as extensive and contemporary applications.