@article {D:RMs, title = {A Strengthening of the {R}escher{\textendash}{M}anor Consequence Relations}, journal = {Logique et Analyse}, volume = {46}, number = {183{\textendash}184}, year = {2003}, pages = {289{\textendash}313}, abstract = {

The flat Rescher{\textendash}Manor consequence relations{\textendash}-the Free, Strong, Weak, C-Based, and Argued consequence relation{\textendash}-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{\textendash}-the comparison with Jaskowski{\textquoteright}s D2 is instructive. The method followed by Joke Meheus to extend D2 to an adaptive logic, may also be applied to the Rescher{\textendash}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.

}, author = {Batens, Diderik} }