Extending Dialectical Classical Logic Argumentation with Unrestricted Rebut and Occam Razor Defeats

Dialectical Classical Logic Argumentation (D-Cl-Arg) formalises maxiconsistent non-monotonic reasoning under the practical assumption that agents have bounded resources for classical inference, and that agents do not typically check arguments’ premises for subset minimality and consistency. However, D-Cl-Arg still satisfies all rationality postulates. Moreover D-Cl-Arg accommodates uses of argument characteristic of dialectical practice. This paper extends D-Cl-Arg to accommodate further dialectical uses of argument; in particular unrestricted rebuts on the deductively derived conclusions of arguments, and Occam Razor defeats that dialectically demonstrate that an argument makes use of redundant premises. We show that all rationality postulates are still satisfied, while relaxing constraints on preference relations that were previously required to prove rationality.