嵌套知识的意识逻辑
Logic of Awareness for Nested Knowledge
AI总结：
本文提出了带划分与链的意识逻辑（ALPC），通过引入不可区分关系和意识的信念链来形式化有限推理能力智能体的嵌套显式知识，并提供了Kripke风格语义、完备的证明系统及其在计算机科学和博弈论中的应用展望。
摘要：
人类的推理能力是有限的。处理人类知识逻辑推理的逻辑学应当反映这些有限的能力。意识逻辑（Logic of awareness）就是其中之一。在该逻辑中，具有有限推理能力的智能体在给定时刻实际知道的内容（显式知识）与智能体通过对其已知内容执行所有可能的推理而获得的理想知识（隐式知识）被区分开来。本文提出了一种针对显式知识的逻辑。特别地，我们更关注嵌套显式知识，即智能体在给定时刻实际知道的关于另一个智能体的知识。我们发展了两种思想的新形式化，并提出了 Kripke 风格的语义。第一种思想是智能体意识状态对其推理能力的影响。我们引入了可能世界上的一个关系，称为不可区分关系，以表示由于缺乏意识而产生的无知。第二种思想是每个智能体在另一个智能体脑海中的意识状态。我们引入了一个非空的智能体有限序列，称为“意识的信念链”。我们的逻辑被称为带划分与链的意识逻辑（ALPC）。通过一个例子，我们展示了如何用我们的逻辑对嵌套显式知识进行形式化。此后，我们提出了证明系统并证明了完备性。最后，我们讨论了扩展和应用我们逻辑的方向并作了总结。我们的逻辑为人类知识的形式化表示提供了基础。我们期望该逻辑能通过描述和分析博弈中的战略行为及实用的智能体通信，应用于计算机科学和博弈论。
英文摘要：
Reasoning abilities of human beings are limited. Logics that treat logical inference for human knowledge should reflect these limited abilities. Logic of awareness is one of those logics. In the logic, what an agent with a limited reasoning ability actually knows at a given moment (explicit knowledge) is distinguished from the ideal knowledge that an agent obtains by performing all possible inferences with what she already knows (implicit knowledge). This paper proposes a logic for explicit knowledge. In particular, we focus more on nested explicit knowledge, which means another agent's knowledge that an agent actually knows at a given moment. We develope a new formalization of two ideas and propose Kripke-style semantics. The first idea is the effect on an agent's reasoning ability by a state of an agent's awareness. We incorporate a relation on possible worlds called an indistinguishable relation to represent ignorance due to lack of awareness. The second idea is a state of each agent's awareness in the other agent's mind. We incorporate a non-empty finite sequence of agents called \textit{a chain of belief for awareness}. Our logic is called Awareness Logic with Partitions and Chains (ALPC). Employing an example, we show how nested explicit knowledge is formalized with our logic. Thereafter, we propose the proof system and prove the completeness. Finally, we discuss directions for extending and applying our logic and conclude. Our logic offers a foundation for a formal representation of human knowledge. We expect that the logic can be applied to computer science and game theory by describing and analyzing strategic behavior in a game and practical agent communication.
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。
