A CONCISE AXIOMATIZATION OF RM
Zachary J. Ernst, Branden Fitelson, Kenneth D. Harris, Larry Wos · 2001
A new axiomatization for the implicational fragment of Dunn’s system RM is given. The new axiomatization is considerably more concise than the axiomatization that was previously known. Speciflcally, we show that the two axioms CCpCpqCpq and CCCCCpqqprCCCCCqppqrr may be replaced with either CCCpCCCqprqrr or CCCCCpqrCqprr. Because the implicational fragment of RM coincides with the implicational fragment of Sobocinski’s system S, the new axiomatization provides a concise basis for that system as well. Let R be the system of relevant implication, and let R! be its implicational fragment. R! is given by the following independent axiom-schema, with the rules modus ponens and substitution [6], p. 88: