A Strengthening of the Rescher–Manor Consequence Relations

TitleA Strengthening of the Rescher–Manor Consequence Relations
Publication TypeJournal Article
Year of Publication2003
AuthorsBatens, D
JournalLogique et Analyse

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 by Joke Meheus 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.

Citation KeyD:RMs
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