A new look at Ternary Boolean Algebras

TL;DR

This paper introduces a novel perspective on ternary Boolean algebras by deriving negation from the ternary operation and relaxing symmetry axioms, offering a fresh algebraic framework.

Contribution

It proposes a new axiomatization of ternary Boolean algebras that does not rely on symmetry, with negation derived from the ternary operation.

Findings

Negation can be derived from the ternary operation.

Symmetry axioms are replaced by alternative axioms.

The new framework broadens the understanding of ternary Boolean algebras.

Abstract

We present a new approach to ternary Boolean algebras in which negation is derived from the ternary operation. The key aspect is the replacement of complete commutativity by other axioms that do not require the ternary operation to be symmetric.