I shall report on two new papers: I) A Dynamic Characterization of the Pure Logic of Relevant Implication. It is known that there are dynamic proofs for consequence relations that are non-monotonic, and also for monotonic consequence relations that lack a positive test. This paper illustrates three interesting points:(i) A set of properties that characterizes an inference relation on the (very natural) dynamic proof interpretation, need not characterize the same inference relation (or even any inference relation) on the usual set-theoretical interpretation.(ii) A proof format may display an internal dynamics (defeasible conclusions) in the absence of an external dynamics (non-monotonicity).(iii) A monotonic logic may have a non-monotonic characterization. II) A Strengthening of the Rescher--Manor Consequence Relations. 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 not-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. Moreover, the extension of the Strong consequence relation seems to offer all one might expect from the Argued consequence relation.