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arXiv 1602.07515quant-ph
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认知语义学的量子方法

Quantum Approach to Epistemic Semantics

Giuseppe Sergioli, Roberto Leporini

摘要:

量子信息提出了量子逻辑的新形式,称为量子计算逻辑,其中句子的含义由量子信息(通常是某些希尔伯特空间的密度算子)表示,这些信息可以通过量子粒子存储和传输。这种方法可以应用于认知逻辑操作的语义表征,这可能发生在句子中,如“在时间t0鲍勃知道,在时间t爱丽丝知道自旋值是”。每个认知主体(比如,Alice,Bob,...)有一个特征性的真值透视,对应于希尔伯特空间C^2的一个特定的标准正交基。从物理学的角度来看,真理视角可以与一种允许人们测量给定可观察物的仪器相关联。表征任何智能体知识的一个重要特征是他/她可访问的信息量(技术上,一组特殊的密度算子,也代表了所讨论的智能体的内部记忆)。我们可以证明,有趣的认知操作是量子信道的特殊例子,它们通常不是幺正的。由于可能的测量程序或关于环境的信息的丢失,了解的行为可能涉及某种内在的不可逆性。我们还说明了一些相对论性的影响,出现在认知代理人的行为。

英文摘要:

Quantum information has suggested new forms of quantum logic, called quantum computational logics, where meanings of sentences are represented by pieces of quantum information (generally, density operators of some Hilbert spaces), which can be stored and transmitted by means of quantum particles. This approach can be applied to a semantic characterization of epistemic logical operations, which may occur in sentences like "At time t0 Bob knows that at time t Alice knows that the spin-value is up". Each epistemic agent (say, Alice, Bob,...) has a characteristic truth-perspective, corresponding to a particular orthonormal basis of the Hilbert space C^2. From a physical point of view, a truth-perspective can be associated to an apparatus that allows one to measure a given observable. An important feature that characterizes the knowledge of any agent is the amount of information that is accessible to him/her (technically, a special set of density operators, which also represents the internal memory of the agent in question). One can prove that interesting epistemic operations are special examples of quantum channels, which generally are not unitary. The act of knowing may involve some intrinsic irreversibility due to possible measurement procedures or to a loss of information about the environment. We also illustrate some relativistic-like effects that arise in the behavior of epistemic agents.

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。

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