We present a formal, mathematical model of argument structure and evaluation, called the Carneades Argumentation Framework, which applies proof standards  to determine the defensibility of arguments and the acceptability of statements on an issue-by-issue basis. Carneades uses three kinds of premises (ordinary premises, presumptions and exceptions) and information about the dialectical status of statements (undisputed, at issue, accepted or rejected) to model critical questions in such a way as to allow the burden of proof to be allocated to the proponent or the respondent, as appropriate.
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