In an adaptive logic APL, based on a (monotonic) non-standardlogic PL the consequences of Γ can be defined in terms ofa selection of the PL-models of Γ. An important property ofthe adaptive logics ACLuN1, ACLuN2, ACLuNs1, andACLuNs2 logics is proved: whenever a model is not selected, this isjustified in terms of a selected model (Strong Reassurance). Theproperty fails for Priest's LP m because its way of measuring thedegree of abnormality of a model is incoherent – correcting thisdelivers the property.