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An argumentation can be the ponens operator applied to two argumentations and . The proofs of M1.8 stated previously are full of such ponens operators.
If the ponens operator is applied to an argumentation which concludes and an argumentation which concludes , then concludes .
When the adaption process is applied to an argumentation of form it will try to ensure that the conclusion of has form . Adaption will do so by instantiating meta-quantifiers and verify side conditions.
When adaption is applied to , it will also do adaption internally in , but it will not try to adapt the outcome of to anything particular.
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