论文标题
关于后条件在动态一阶认识逻辑中的作用
On the Role of Postconditions in Dynamic First-Order Epistemic Logic
论文作者
论文摘要
动态认知逻辑（DEL）是一种逻辑，它通过使用前后条件的动作模型在多代理设置中建模信息。在最近的一项工作中，DEL已扩展到一阶认知逻辑（DFOEL），并证明了由此产生的认知计划问题是可以决定的，只要行动模型前后的条件是非模式，并且一阶域是有限的。我们的贡献凸显了后条件在DFOEL中的作用。我们表明，如果非模式事件后条件可能包含一阶量词，则可能是无限的一阶域的认知计划问题是不确定的，而相反，当事件后条件是无量词的情况下，问题就可以决定。后一个结果是非平凡的，并且广泛使用自动结构。
Dynamic Epistemic Logic (DEL) is a logic that models information change in a multi-agent setting through the use of action models with pre- and post-conditions. In a recent work, DEL has been extended to first-order epistemic logic (DFOEL), with a proof that the resulting Epistemic Planning Problem is decidable, as long as action models pre- and post-conditions are non-modal and the first-order domain is finite. Our contribution highlights the role post-conditions have in DFOEL. We show that the Epistemic Planning Problem with possibly infinite first-order domains is undecidable if the non-modal event post-conditions may contain first-order quantifiers, while, on the contrary, the problem becomes decidable when event post-conditions are quantifier-free. The latter result is non-trivial and makes an extensive use of automatic structures.
