关于Belnap-Dunn模态逻辑的量化形式及其某些扩展
On the quantified version of the Belnap-Dunn modal logic and some extensions of it
摘要：
我们考虑一个量化版本的（命题）模态逻辑$\mathsf{BK}$，提出了较早的S。P. Odintsov和H. Wansing;该版本将用$\mathsf{QBK}$表示。利用规范模型方法，我们证明了$\mathsf{QBK}$关于一个合适的可能世界语义的强完备性。对于某些自然的$\mathsf{QBK}$ -扩张也得到了类似的结果。特别地，证明了用Barcan方案对$\mathsf{QBK}$的扩展对于具有常数域的适当可能世界语义是强完全的。此外，我们定义忠实的嵌入（à la Gödel-McKinsey-Tarski）的量化版本的纳尔逊的建设性逻辑到适当的$\mathsf{QBK}$ -扩展。
英文摘要：
We consider a quantified version of the (propositional) modal logic $\mathsf{BK}$, proposed earlier by S. P. Odintsov and H. Wansing; this version will be denoted by $\mathsf{QBK}$. Using the canonical model method, we prove the strong completeness of $\mathsf{QBK}$ with respect to a suitable possible world semantics with expanding domains. Similar results are obtained for some natural $\mathsf{QBK}$-extensions. In particular, it is proved that the extension of $\mathsf{QBK}$ with Barcan scheme is strongly complete with respect to a suitable possible world semantics with constant domains. Moreover, we define faithful embeddings (à la Gödel-McKinsey-Tarski) of the quantified versions of Nelson's constructive logics into appropriate $\mathsf{QBK}$-extensions.
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