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A first-order epistemic quantum computational semantics with relativistic-like epistemic effects

机译：具有相对论似的认知效应的一阶认知量子计算语义

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摘要

Quantum computation has suggested new forms of quantum logic, called quantum computational logics. In these logics well-formed formulas are supposed to denote pieces of quantum information: possible pure states of quantum systems that can store the information in question. At the same time, the logical connectives are interpreted as quantum logical gates: unitary operators that process quantum information in a reversible way, giving rise to quantum circuits. Quantum computational logics have been mainly studied as sentential logics(whose alphabet consists of atomic sentences and of logical connectives). In this article we propose a semantic characterization for a first-order epistemic quantum computational logic, whose language can express sentences like "Alice knows that everybody knows that she is pretty". One can prove that (unlike the case of logical connectives) both quantifiers and epistemic operators cannot be generally represented as (reversible) quantum logical gates. The "act of knowing" and the use of universal (or existential) assertions seem to involve some irreversible "theoretic jumps", which are similar to quantum measurements. Since all epistemic agents are characterized by specific epistemic domains(which contain all pieces of information accessible to them), the unrealistic phenomenon of logical omniscience is here avoided: knowing a given sentence does not imply knowing all its logical consequences. (c) 2015 Elsevier B.V. All rights reserved.
机译：量子计算提出了新形式的量子逻辑，称为量子计算逻辑。在这些逻辑中，格式良好的公式应该表示量子信息：可以存储所讨论信息的量子系统的可能纯态。同时，逻辑连接词也被解释为量子逻辑门：unit运算符以可逆的方式处理量子信息，从而产生了量子电路。量子计算逻辑主要作为句子逻辑进行研究（其字母由原子句子和逻辑连接词组成）。在本文中，我们提出了一阶认知量子计算逻辑的语义表征，该语言的语言可以表达诸如“爱丽丝知道每个人都知道她很漂亮”之类的句子。可以证明（不同于逻辑连接词的情况），量词和认知运算符都不能普遍表示为（可逆的）量子逻辑门。 “知道的行为”和使用通用（或存在）断言似乎涉及一些不可逆的“理论跃迁”，类似于量子测量。由于所有认知主体都具有特定的认知领域（包含可访问的所有信息）的特征，因此在这里避免了逻辑全知的不现实现象：知道给定的句子并不意味着知道其所有逻辑后果。 （c）2015 Elsevier B.V.保留所有权利。

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