02170946

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02170946 Batens, Diderik A strengthening of the Rescher-Manor consequence relations. Log. Anal., Nouv. S\'er. 46, No. 183-184, 289-313 (2003). 2003 Centre National Belge de Recherches de Logique, Bruxelles EN paraconsistent logic discussive logic flat Rescher-Manor consequence relations maximal consistent subsets Summary: The flat Rescher-Manor consequence relations -- the Free, Strong, Weak, C-Based, and Argued consequence relations -- 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 $\sim\!\! A$). The five consequence relations may be applied to discussive situations as intended by Ja\'skowski -- the comparison with Ja\'skowski's D2 is instructive. The method followed by {\it J. Meheus} [``An adaptive logic based on Ja\'skowski's D2'' (to appear)] 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.