信息不完备下的知识遗忘

Knowledge Forgetting under Incomplete Information

智能体不仅仅要具备知识学习的能力,还应具备知识遗忘的能力。智能体关于客观世界的信息往往是不完备的,探索信息不完备环境下的知识遗忘问题显得尤为重要。模态谓词逻辑适用于信息不完备环境下智能体知识的不确定性表示和推理,故将知识遗忘的定义扩展到模态谓词逻辑,并分析其基础性质。一般情况下,一阶模态逻辑中知识遗忘是不可定义的。因此,一阶模态逻辑的一个片段被给出,其具有较强的表达能力,且该片段的公式遗忘原子命题是一阶模态逻辑可定义的,遗忘谓词是二阶模态逻辑可定义的。

An intelligent agent should possess not only the ability of knowledge learning but also the ability of knowledge forgetting. An agent’s information about the world is always incomplete. It is significant to explore the problem of knowledge forgetting under incomplete information. Modal predicate logic is taken to represent the knowledge base of an agent with incomplete information. Knowledge forgetting in modal predicate logic is defined, and its basic properties are analyzed. In general, knowledge forgetting is indefinable in first order modal logic. A fragment of first-order modal logic is identified. For formulas of the fragment, forgetting an atom is definable in first-order modal logic, and forgetting a predicate is definable in second-order modal logic. The fragment goes beyond formulas without quantifying-in, and is suitable for representing agents' knowledge in many cases.