A *logic* is a pair (*P,Q*) where *P* is a set of formulas of a fixed propositional language and *Q* is a set of rules. A formula α is *deducible* from *X* in the logic (*P, Q*) if it is deducible from *X*∪*P**via**Q.* A matrix
$$\mathfrak{M}$$
is *strongly adequate* to (*P, Q*) if for any *α, X, α* is deducible from *X* iff for every valuation in
$$\mathfrak{M}$$
, α is designated whenever all the formulas in *X* are. It is proved in the present paper that if *Q* = *{modus ponens, adjunction }* and *P* ε {*E, R, E*^{+}, *R*^{+}, *E*^{I}, *R*^{I} } then there exists a matrix strongly adequate to (*P, Q*).