Abstract: We discuss five kinds of representations of rationales and provide a formal account of how they can alter disputation. The formal model of disputation is derived from recent work in argument. The five kinds of rationales are compilation rationales, which can be represented without assuming domain-knowledge (such as utilities) beyond that normally required for argument. The principal thesis is that such rationales can be analyzed in a framework of argument not too different from what AI already has. The result is a formal understanding of rationales, a partial taxonomy, and a foundation for computer programs that represent and reason with rationales. The five kinds of rationales are as follows: (c)ompression and (s)pecialization, which yield rules, and (d)isputation, which yields a decision. These are modeled as potentially changing the focus of the dispute. Then there are (f)it, a rationale for rules, and (r)esolution, a rationale for decisions. These cannot be modeled as simply; they force disputation to a meta-level, at least temporarily. The paper first discusses each kind of rationale in the abstract. Then it produces a model of dispute in which the simpler rationales can be analyzed. Formal examples are given. The model is augmented to allow analysis of the more difficult rationales. Examples are again given. The discussion is not intended to be strictly mathematical; rather, it aims to use formal methods to illuminate and provide framework for future interpretation and implementation.