 An adaptive logic is a logic that adapts itself to the situation at the time of application of inference rules. It models the dynamics of our reasoning. There are two senses in which reasoning is dynamic: external and internal. Reasoning is externally dynamic if as new information becomes available expanding the premise set, consequences inferred previously may have to be withdrawn. The external dynamics is thus the non-monotonic character of some consequence relations: \(\Gamma \vdash A\) and \(\Gamma \cup \Delta \not\vdash A\) for some \(\Gamma , \Delta\) and \(A\). However, even if the premise-set remains constant, some previously inferred conclusion may be considered as not derivable at a later stage. As our reasoning proceeds from a premise set, we may encounter a situation where we infer a consequence provided that no abnormality, in particular no contradiction, obtains at some stage of the reasoning process. If we are forced to infer a contradiction at a later stage, our reasoning has to adapt itself so that an application of the previously used inference rule is withdrawn. In such a case, reasoning is internally dynamic. Our reasoning may be internally dynamic if the set of valid inferences is not recursively enumerable (i.e., there is no decision procedure that leads to ‘yes’ after finitely many steps if the inference is indeed valid). It is the internal dynamics that adaptive logics are devised to capture.