A strengthening of the Rescher–Manor consequence relations

Diderik Batens


The flat Rescher–Manor consequence relations — the Free, Strong, Weak, C-Based, and Argued consequence relation — are defined in terms of the classical consequences of the maximal consistent subsets of (possibly) inconsistent sets of premises. If the premises are inconsistent, the Free, Strong and C-Based consequence sets are consistent and the Argued consequence set avoids explicit inconsistencies (such as A and ~A).
The five consequence relations may be applied to discussive situations as intended by Jaskowski — the comparison with Jaskowski’s D2 is instructive. The method followed in [12] to extend D2 to an adaptive logic, may also be applied to the Rescher–Manor consequence relations. It leads to an extension of the Free, Strong, Weak, and C-Based consequence relations. The extended consequence sets are consistent and closed under Classical Logic. Applying the method to the Argued consequence relation leads to a different consequence relation, not an extension. Neither the Argued consequence relation nor its extension appear very interesting in the present application context.

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