D-complete Single Axioms for the Equivalential Calculus with the rules D and R
Marcin Czakon · Bulletin of the Section of Logic · 2024
Ulrich showed that most of the known axiomatisations of the classical equivalence calculus (EC) are D-incomplete, that is, they are not complete with the condensed detachment rule (D) as the primary rule of the proof procedure. He proved that the axiomatisation EEpEqrErEqp, EEEpppp by Wajsberg is D-complete and pointed out a number of D-complete single axioms, including one organic single axiom. In this paper we present new single axioms for EC with the condensed detachment and the reversed condensed detachment rules that form D-complete bases and are organic.