In almost all cases, one must add operations to the \(+\) and \(\cdot\) of \({\textsf{J}}_0\), along with axioms capturing their intended behavior. The exception is factivity, discussed next, for which no additional operations are required, though additional axioms are. It is always understood that constant specifications cover axioms from the enlarged set. We continue using the terminology of Section 2.3; for instance a constant specification is axiomatically appropriate if it meets the condition as stated there, for all axioms including any that have been added to the original set. Theorem 1 from Section 2.3 continues to apply to our new justification logics, and with the same proof: if we have a justification logic \(\textsf{JL}_{CS}\) with an axiomatically appropriate constant specification, Internalization holds.