Deflog: On the logical interpretation of prima facie justified assumptions

Assumptions are often not considered to be definitely true, but only as prima facie justified. When an assumption is prima facie justified, there can for instance be a reason against it, by which the assumption is not actually justified. The assumption is then said to be defeated. This requires a revision of the standard conception of logical interpretation of sets of assumptions in terms of their models. Whereas in the models of a set of assumptions, all assumptions are taken to be true, an interpretation of prima facie justified assumptions must distinguish between the assumptions that are actually justified in the interpretation and those that are defeated. In the present paper, the logical interpretation of prima facie justified assumptions is investigated. The central notion is that of a dialectical interpretation of a set of assumptions. The basic idea is that a prima facie justified assumption is not actually justified, but defeated when its so-called dialectical negation is justified. The properties of dialectical interpretation are analysed by considering partial dialectical interpretations, or stages, and by establishing the notion of dialectical justification. The latter leads to a characterization of the existence and multiplicity of the dialectical interpretations of a set of assumptions. Since dialectical interpretations are a variant of stable semantics, the results are relevant for existing work on nonmonotonic logic and defeasible reasoning, on which the present work builds. Instead of focusing on defeasible rules or arguments, the present approach is sentence-based. A particular innovation is the use of a conditional that is prima facie justified (just like other assumptions) instead of an inconclusive conditional.