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.
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Acknowledgements
Vitor Greati acknowledges support from the FWF project P33548. Sérgio Marcelino’s research was done under the scope of project FCT/MCTES through national funds and when applicable co-funded by EU under the project UIDB/50008/2020.
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Special Issue: Strong and weak Kleene logics Edited by Gavin St. John and Francesco Paoli
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Greati, V., Marcelino, S. & Rivieccio, U. Finite Hilbert Systems for Weak Kleene Logics. Stud Logica (2024). https://doi.org/10.1007/s11225-023-10079-w
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DOI: https://doi.org/10.1007/s11225-023-10079-w