具有常识的任意箭头更新逻辑既不是RE也不是co-RE
Arbitrary Arrow Update Logic with Common Knowledge is neither RE nor co-RE
摘要：
具有公共知识的任意箭头更新逻辑（Arbitrary Arrow Update Logic with Common Knowledge，AAULC）是一种动态认知逻辑，具有（i）表示特定类型的信息变化的箭头更新运算符和（ii）量化箭头更新的任意箭头更新运算符。通过将图灵机的执行过程编码到AAULC中，我们证明了AAULC中的有效公式和可满足公式都不是递归可重算的。特别是，它遵循AAULC没有递归公理化。
英文摘要：
Arbitrary Arrow Update Logic with Common Knowledge (AAULC) is a dynamic epistemic logic with (i) an arrow update operator, which represents a particular type of information change and (ii) an arbitrary arrow update operator, which quantifies over arrow updates. By encoding the execution of a Turing machine in AAULC, we show that neither the valid formulas nor the satisfiable formulas of AAULC are recursively enumerable. In particular, it follows that AAULC does not have a recursive axiomatization.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
