 In order to illustrate the idea behind adaptive logics, consider the premise set \(\Gamma = \{p, \neg p \vee r, \neg r \vee s, \neg s, s \vee t\}\). One may start reasoning with \(\neg s\) and \(s \vee t\), using the Disjunctive Syllogism (DS) to infer \(t\), given that \(s \wedge \neg s\) does not obtain. We then reason with \(p\) and \(\neg p \vee r\), to infer \(r\) with the DS, given that \(p \wedge \neg p\) does not obtain. Now, we can apply the DS to \(\neg r \vee s\) and \(r\) to derive \(s\), provided that \(r \wedge \neg r\) does not obtain. However, by conjoining \(s\) and \(\neg s\), we can obtain \(s \wedge \neg s\). Hence we must withdraw the first application of DS, and so the proof of \(t\) lapses. A consequence of this reasoning is what cannot be defeated at any stage of the process.