Argumentation systems aim to reflect how conflicting information is used in cognition to construct and analyse arguments. So these systems involve identifying arguments and counterarguments relevant to an issue (e.g. What are the pros and cons for the safety of mobile phones for children?). They may also involve weighing, comparing, or evaluating arguments (e.g. What sense can we make of the arguments concerning mobile phones for children?) and they may involve drawing conclusions (e.g. A parent answering the question ``Are mobile phones safe for my children?"). In addition, they may involve convincing an audience (e.g. A politician making the case that mobile phones should be banned for children because the risk of radiation damage is too great). In this talk, I cover some of the basics of the theory and implementation of logic-based argumentation systems and then cover some work we are doing on an application in analysing evidence from clinical drug trials on treatments for breast cancer.