On axiom systems of Słupecki for the functionally complete three-valued logic

Mateusz M. Radzki

pp. 403-415

in: Axiomathes 27 (4), 2017.

Abstract

The article concerns two axiom systems of Słupecki for the functionally complete three-valued propositional logic: W1–W6 (from 1936) and A1–A9 (from 1946). The article proves that both of them are inadequate—W1–W6 is semantically incomplete, on the other hand, A1–A9 governs a functionally incomplete calculus, and thus, it cannot be a semantically complete axiom system for the functionally complete three-valued logic.