Abstract
Dyrda and Prucnal gave a Hilbert-style axiomatization for the \(\{\wedge ,\vee \}\)-fragment of classical propositional logic. Their proof of completeness follows a different approach to the standard one proving the completeness of classical propositional logic. In this note, we present an alternative proof of Dyrda and Prucnal’s result following the standard arguments which prove the completeness of classical propositional logic.
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This work was partially supported by FONCyT-ANPCyT (Argentina) under the Grant PICT-2019-00674, by Universidad Nacional de La Pampa under the Grant P.I. No 78M, Res. 523/19, and by FONCyT-ANPCyT (Argentina) under the Grant PICT-2019-00882.
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González, L.J. An alternative proof of the Hilbert-style axiomatization for the \(\{\wedge ,\vee \}\)-fragment of classical propositional logic. Arch. Math. Logic 61, 859–865 (2022). https://doi.org/10.1007/s00153-022-00815-9
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DOI: https://doi.org/10.1007/s00153-022-00815-9