English

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.

Keywords

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

R2 v1 2026-06-28T14:10:14.659Z