Abstract

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 is deducible from X in the logic (P, Q) if it is deducible from XP via Q. A matrix is strongly adequate to (P, Q) if for any , X, is deducible from X iff for every valuation in , is designated whenever all the formulas in X are. It is proved in the present paper that if Q = {modus ponens, adjunction } and P {E, R, E +, R +, E I, R I } then there exists a matrix strongly adequate to (P, Q).