Finite Hilbert Systems for Weak Kleene Logics

V. Greati, S. Marcelino, U. Rivieccio
Studia Logica

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.

  • (20/03/2024) Corrections on Def. 2, Def. 3 (PWK system) and Rem. 4. The previous PWK system in Def. 3 was not conforming with the recipe in Def. 2, now it does. Check the arXiv version here from 21/03/2024 for the updated version. The journal publication will be updated soon.