论文标题
可解释性逻辑$ \ mathbf {il} $的sublogics的模态完整性
Modal completeness of sublogics of the interpretability logic $\mathbf{IL}$
论文作者
论文摘要
我们研究了几种可解释性逻辑$ \ mathbf {il} $的sublogics的模态完整性和不完整性。我们介绍了sublogic $ \ mathbf {il}^ - $，并证明$ \ mathbf {il}^ - $相对于维瑟（Visser）引入的Veltman Prestructures而言是合理的。此外，我们证明了$ \ mathbf {il}^ - $和$ \ mathbf {il} $之间的十二逻辑的模态完整性。另一方面，我们证明了$ \ mathbf {il} $的八个天然sbrogics是模样不完整的。最后，我们证明这些不完整的逻辑是关于广义veltman Prestructures的完整逻辑。由于这些研究的结果，我们获得了本文研究的二十个逻辑都是可决定的。
We study modal completeness and incompleteness of several sublogics of the interpretability logic $\mathbf{IL}$. We introduce the sublogic $\mathbf{IL}^-$, and prove that $\mathbf{IL}^-$ is sound and complete with respect to Veltman prestructures which are introduced by Visser. Moreover, we prove the modal completeness of twelve logics between $\mathbf{IL}^-$ and $\mathbf{IL}$ with respect to Veltman prestructures. On the other hand, we prove that eight natural sublogics of $\mathbf{IL}$ are modally incomplete. Finally, we prove that these incomplete logics are complete with respect to generalized Veltman prestructures. As a consequence of these investigations, we obtain that the twenty logics studied in this paper are all decidable.
