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arXiv · 2401.03265

Finite Hilbert systems for Weak Kleene logics

Vitor Greati·Sérgio Marcelino·Umberto Rivieccio
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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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Vitor Greati, Sérgio Marcelino, Umberto Rivieccio. 2024-01-06. Finite Hilbert systems for Weak Kleene logics. https://doi.org/10.1007/s11225-023-10079-w

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