#3815. Modal and Intuitionistic Variants of Extended Belnap–Dunn Logic with Classical Negation

October 2026publication date
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Computer Science (miscellaneous);
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Abstract:
In this study, we introduce Gentzen-type sequent calculi BDm and BDi for a modal extension and an intuitionistic modification, respectively, of De and Omori’s extended Belnap–Dunn logic BD+ with classical negation. We prove theorems for syntactically and semantically embedding BDm and BDi into Gentzen-type sequent calculi S4 and LJ for normal modal logic and intuitionistic logic. The cut-elimination, decidability, and completeness theorems for BDm and BDi are obtained using these embedding theorems.
Keywords:
Belnap–Dunn logic; Completeness theorem; Cut-elimination theorem; Embedding theorem; Sequent calculus

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