Ariana Karina Molina Campoverde

Arianean Arithmetic: Peano Arithmetic over Belnap's Four-Valued Logic

2026 · Zenodo (CERN European Organization for Nuclear Research)

We introduce Arianean Arithmetic, a semantic extension of classical Peano Arithmetic based on Belnap's four-valued logic FOUR = {T, F, N, B}. The syntactic structure and proof theory of arithmetic remain entirely classical. The extension …