Аннотация:The central result of this paper arose within the context of astudy of the problem of transfer from implicative-negative logical
systems. This paper has been inspired by one of the ideas of the paper by A. Arruda. This idea is that a propositional variable is interpreted as some implicative formula, but propositional variable negation is interpreted as inversion of the formula which interprets this propositional variable. As we see it, the given interpretation of propo- sitional variables and their negations opens the opportunity to enrich implication theories by such negations, the nature of which is essentially defined by these theories. We are building a calculus Cl: and showing (see theorem 5) that the set of all formulas being deduced in Cl is the least implicative-negative logic with inverse negation, the latter being adequate to the implication of the classical implicative logic. In this paper a sequential version GCl of the calculus Cl is presented, the decidability and paraconsistency of Cl is established,
the connection of Cl with the calculus VI of A. Arruda and with the calculus PIL of D. Batens is considered.