An alternative proof of the Hilbert-style axiomatization for the \(\{\wedge ,\vee \}\)-fragment of classical propositional logic

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.