Some Results Concerning Axioms for Equivalential Calculus

Marcin Czakon

doi:10.18778/0138-0680.2025.05

Authors

Marcin Czakon John Paul II Catholic University of Lublin, Department of Logic https://orcid.org/0000-0001-6217-6640

DOI:

https://doi.org/10.18778/0138-0680.2025.05

Keywords:

equivalential calculus, D-complete, R-complete, single axiom, condensed detachment

Abstract

One of the most important questions in the area of the equivalential calculus (EC) currently is the issue of the single shortest axiom. We show some new a single organic and inorganic axioms for EC which are either D-complete or R-complete. We also present a number of two-element sets of axioms which posses some special properties. Two matrix are also discussed, which exclude two formulas from the set of potential 2MP-complete axioms.

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