Axioms of Propositional Logic with as few negation axioms as possible

Question

Could you direct me to an axiom system for propositional logic over the connectives $\land$, $\lor$, and $\lnot$ with as few axioms over negation as reasonably possible? I've done a fair bit of googling and what comes up seems non-minimal.

I'm not expecting something provably minimal, just some suggestions that are more elegant than most of what's out there.

Answer 1

I'll use Polish notation. We don't need both A, and K, since both {A, N} and {K, N} form a complete set of connectives. Here's three A-N systems with a single axiom... all of them have {AN$\alpha$$\beta$, $\alpha$} $\vdash$ $\beta$ as their rule of inference in addition to uniform substitution.

1. ANANANpqArAstANANspArAtp.
2. ANANANpqArAstANANtsArAps.
3. ANANANpqArAstANANrpAtAsp.

All of these come from C. A. Meredith's 1953 paper on single axioms, referenced from A. N. Prior's Formal Logic p. 305, 1962, 2nd edition.