Abstract:
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, quantification.
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