Geodesic
On the quantified version of the Belnap--Dunn modal logic
Sbornik. Mathematics, Tome 215 (2024) no. 3, pp. 323-354

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We develop a quantified version of the propositional modal logic $\mathsf{BK}$ from an article by Odintsov and Wansing, which is based on the (non-modal) Belnap–Dunn system; we denote this version by $\mathsf{QBK}$. First, by using the canonical model method we prove that $\mathsf{QBK}$, as well as some important extensions of it, is strongly complete with respect to a suitable possible world semantics. Then we define translations (in the spirit of Gödel–McKinsey–Tarski) that faithfully embed the quantified versions of Nelson's constructive logics into suitable extensions of $\mathsf{QBK}$. In conclusion, we discuss interpolation properties for $\mathsf{QBK}$-extensions. Bibliography: 21 titles.
Keywords: modal logic, constructive logic, strong negation, possible world semantics
Mots-clés : quantification. 
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     title = {On the quantified version of the {Belnap--Dunn} modal logic},
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A. V. Grefenshtein; S. O. Speranski. On the quantified version of the Belnap--Dunn modal logic. Sbornik. Mathematics, Tome 215 (2024) no. 3, pp. 323-354. http://geodesic.mathdoc.fr/item/SM_2024_215_3_a2/