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This thesis describes some of the problems in providing care for patients with breast cancer. These are then used to motivate the development of an extension to an existing theory of argumentation, which I call the Ontology-based Argumentation Formalism (OAF). The work is assessed in both theoretical and empirical ways. From a clinical perspective, there is a problem with the provision of care. Numerous reports have noted the failure to provide uniformly high quality care, as well as the number of deaths caused by medical care. The medical profession has responded in various ways, but one of these has been the development of Decision Support Systems (DSS). The evidence for the effectiveness of such systems is mixed, and the technical basis of such systems remains open to debate. However, one basis that has been used is argumentation. An important aspect of clinical practice is the use of the evidence from clinical trials, but these trials are based on the results in defined groups of patients. Thus when we use the results of clinical trials to reason about treatments, there are two forms of information we are interested in - the evidence from trials and the relationships between groups of patients and treatments. The relational information can be captured in an ontology about the groups of patients and treatments, and the information from the trials captured as a set of defeasible rules. OAF is an extension of an existing argumentation system, and provides the basis for an argumentation-based Knowledge Representation system which could serve as the basis for future DSS. In OAF, the ontology provides a repository of facts, both asserted and inferred on the basis of formulae in the ontology, as well as defining the language of the defeasible rules. The defeasible rules are used in a process of defeasible reasoning, where monotonic consistent chains of reasoning are used to draw plausible conclusions. This defeasible reasoning is used to generate arguments and counter-arguments. Conflict between arguments is defined in terms of inconsistent formulae in the ontology, and by using existing proposals for ontology languages we are able to make use of existing proposals and technologies for ontological reasoning. There are three substantial areas of novel work: I develop an extension to an existing argumentation formalism, and prove some simple properties of the formalism. I also provide a novel formalism of the practical syllogism and related hypothetical reasoning, and compare my approach to two other proposals in the literature. I conclude with a substantial case study based on a breast cancer guideline, and in order to do so I describe a methodology for comparing formal and informal arguments, and use the results of this to discuss the strengths and weaknesses of OAF. In order to develop the case study, I provide a prototype implementation. The prototype uses a novel incremental algorithm to construct arguments and I give soundness, completeness and time-complexity results. The final chapter of the thesis discusses some general lessons from the development of OAF and gives ideas for future work.