Finite Hilbert systems for Weak Kleene logics
Logic
2024-03-21 v2 Logic in Computer Science
Abstract
Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar-Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics.
Cite
@article{arxiv.2401.03265,
title = {Finite Hilbert systems for Weak Kleene logics},
author = {Vitor Greati and Sérgio Marcelino and Umberto Rivieccio},
journal= {arXiv preprint arXiv:2401.03265},
year = {2024}
}
Comments
Corrections on Def.2, Def.3 (PWK system) and Rem. 4