# 自动认识逻辑

## 语义

${\displaystyle \Box x}$ 为假: 通过这个假定，因为 ${\displaystyle \Box x\rightarrow x}$ 等价于 ${\displaystyle \neg \Box x\vee x}$，而 ${\displaystyle \neg \Box x}$ 被假定为真，${\displaystyle T}$ 成为重言式；所以 ${\displaystyle x}$ 没有被蕴涵。这个结果符合在 ${\displaystyle \Box x}$ 为假中所暗含的假定，就是说 ${\displaystyle x}$ 当前是未知的。所以 ${\displaystyle \Box x}$ 为假的假定是一个展开。

${\displaystyle \Box x}$ 为真: 通过这个假定，${\displaystyle T}$ 蕴涵 ${\displaystyle x}$；所以在 ${\displaystyle \Box x}$ 为真中所暗含的初始假定，就是说 ${\displaystyle x}$ 为真是已知的，被满足了。作为结果，这是另一个展开。

## 引用

• G. Gottlob (1995). Translating default logic into standard autoepistemic logic. Journal of the ACM, 42:711-740.
• T. Janhunen (1998). On the intertranslatability of autoepistemic, default and priority logics. In Proceedings of the Sixth European Workshop on Logics in Artificial Intelligence (JELIA'98), pages 216-232.
• W. Marek and M. Truszczynski (1991). Autoepistemic logic. Journal of the ACM, 38(3):588-619.
• R. C. Moore (1985). Semantical considerations on nonmonotonic logic. Artificial Intelligence, 25:75-94.
• I. Niemelä (1988). Decision procedure for autoepistemic logic. In Proceedings of the Ninth International Conference on Automated Deduction (CADE'88), volume 310 of Lecture Notes in Computer Science, pages 675-684. Springer.