作为计算复杂性问题的逻辑全知

Sergei N. Artëmov, R. Kuznets
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引用次数: 45

摘要

逻辑全知特征假设一个认知主体知道她的假设的所有逻辑结果。本文提供了一个将逻辑全知视为计算复杂性问题的一般理论框架。我们建议采用以下方法:我们假设代理的知识由一个认知逻辑系统E表示;如果已知任何类型为F的有效知识断言A,在A的大小中可以在多项式时间内找到F在E中的证明,我们称这样的代理在逻辑上不是全知的。我们表明,由知识和信念的主要模态逻辑表示的代理在逻辑上是全知的,而由证明逻辑系统表示的代理在逻辑上不是全知的,关于t是F的证明。
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Logical omniscience as a computational complexity problem
The logical omniscience feature assumes that an epistemic agent knows all logical consequences of her assumptions. This paper offers a general theoretical framework that views logical omniscience as a computational complexity problem. We suggest the following approach: we assume that the knowledge of an agent is represented by an epistemic logical system E; we call such an agent not logically omniscient if for any valid knowledge assertion A of type F is known, a proof of F in E can be found in polynomial time in the size of A. We show that agents represented by major modal logics of knowledge and belief are logically omniscient, whereas agents represented by justification logic systems are not logically omniscient with respect to t is a justification for F.
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