论文标题
非著作模态逻辑是结构性的
Non-iterative Modal Logics are Coalgebraic
论文作者
论文摘要
如果可以通过不嵌套模态运算符的公理来定义它，则模态逻辑是\ emph {non-Iliterative}，如果公理中的所有命题变量均在模态运算符的范围内，并且\ emph {rank-1}。众所周知，每个句法定义的等级-1模态逻辑都可以配备典型的colgebraic语义，从而确保合理性和强烈的完整性。在目前的工作中，我们将此结果扩展到非著作模态逻辑，这表明每个非著作模态逻辑都可以配备根据互求功能的规范界面语义，再次确保通过规范模型构建确保健全和强大的完整性。与Rank-1情况下一样，规范的煤层语义等于具有适当框架条件的邻里语义，因此暗示了对邻里语义上的非著作模态逻辑的强烈完整性。作为这些结果的例证，我们与事实分离讨论了能态逻辑，该逻辑是由非著作但不等级〜1的公理捕获的。
A modal logic is \emph{non-iterative} if it can be defined by axioms that do not nest modal operators, and \emph{rank-1} if additionally all propositional variables in axioms are in scope of a modal operator. It is known that every syntactically defined rank-1 modal logic can be equipped with a canonical coalgebraic semantics, ensuring soundness and strong completeness. In the present work, we extend this result to non-iterative modal logics, showing that every non-iterative modal logic can be equipped with a canonical coalgebraic semantics defined in terms of a copointed functor, again ensuring soundness and strong completeness via a canonical model construction. Like in the rank-1 case, the canonical coalgebraic semantics is equivalent to a neighbourhood semantics with suitable frame conditions, so the known strong completeness of non-iterative modal logics over neighbourhood semantics is implied. As an illustration of these results, we discuss deontic logics with factual detachment, which is captured by axioms that are non-iterative but not rank~1.
