论文标题
在Belnap-Dunn模态逻辑的量化版本上
On the quantified version of the Belnap-Dunn modal logic and some extensions of it
论文作者
论文摘要
我们考虑了（命题）模态逻辑$ \ mathsf {bk} $的量化版本，该版本由S. P. Odintsov和H. Wansing提出。此版本将用$ \ mathsf {qbk} $表示。使用规范模型方法，我们证明了$ \ mathsf {qbk} $的强大完整性，相对于具有扩展域的合适世界语义。对于某些天然$ \ mathsf {qbk} $ - 扩展，也获得了类似的结果。特别是，证明使用Barcan方案的$ \ Mathsf {QBK} $扩展在具有恒定域的合适的世界语义方面非常强烈。此外，我们将尼尔森的建设性逻辑的量化版本定义为适当的$ \ mathsf {qbk} $扩展名，将忠实的嵌入（àlaGödel-Mckinsey-tarski）定义为量化版本。
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.
