忘记复杂的命题
Forgetting complex propositions
摘要：
本文使用可能世界语义模型的变化，可能会发生在代理的知识，因为她失去了信息。这建立在以前的工作中，代理人可能会忘记一个原子命题的真值，更一般的情况下，她可能会忘记一个命题公式的真值。这种泛化带来了一些挑战，因为为了忘记一个复杂命题$π$是否是这种情况，智能体也必须丢失关于出现在其中的命题原子的信息，而且没有明确的方法来解决这个问题。我们通过考虑$[\boldsymbol{\ddagger} π]φ$形式的表达式来解决这种情况，该表达式量化了所有可能的（但最小的）忘记是否是$π$的方式。命题原子在所有可能的世界中被非确定性地修改，尽管是一致的。然后，我们表示这在行动模型逻辑，以提供一个健全的和完整的公理化的逻辑知识和遗忘。最后，讨论了一些变体，例如当代理忘记$π$（而不是忘记是否是$π$）时，以及当原子事实的修改在整个模型中不一致时。
英文摘要：
This paper uses possible-world semantics to model the changes that may occur in an agent's knowledge as she loses information. This builds on previous work in which the agent may forget the truth-value of an atomic proposition, to a more general case where she may forget the truth-value of a propositional formula. The generalization poses some challenges, since in order to forget whether a complex proposition $π$ is the case, the agent must also lose information about the propositional atoms that appear in it, and there is no unambiguous way to go about this. We resolve this situation by considering expressions of the form $[\boldsymbol{\ddagger} π]φ$, which quantify over all possible (but minimal) ways of forgetting whether $π$. Propositional atoms are modified non-deterministically, although uniformly, in all possible worlds. We then represent this within action model logic in order to give a sound and complete axiomatization for a logic with knowledge and forgetting. Finally, some variants are discussed, such as when an agent forgets $π$ (rather than forgets whether $π$) and when the modification of atomic facts is done non-uniformly throughout the model.
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。
