Unification of Two Approaches to Quantum Logic: Every Birkhoff – von Neumann Quantum Logic is a Partial Infinite-Valued Łukasiewicz Logic

Jarosław Pykacz

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Unification of Two Approaches to Quantum Logic: Every Birkhoff – von Neumann Quantum Logic is a Partial Infinite-Valued Łukasiewicz Logic

机译：两种量子逻辑方法的统一：每个Birkhoff – von Neumann量子逻辑都是部分无穷大的Łukasiewicz逻辑

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In the paper it is shown that every physically sound Birkhoff – von Neumann quantum logic, i.e., an orthomodular partially ordered set with an ordering set of probability measures can be treated as partial infinite-valued Łukasiewicz logic, which unifies two competing approaches: the many-valued, and the two-valued but non-distributive, which have co-existed in the quantum logic theory since its very beginning.

机译：本文表明，每个物理上健全的伯克霍夫–冯·诺伊曼量子逻辑，即带有概率测度排序集的正交模部分有序集，都可以看作是部分无限值Łukasiewicz逻辑，它将两种相互竞争的方法统一起来：自从一开始就在量子逻辑理论中并存，并且具有二值但非分布。

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《Studia Logica》 |2010年第2期|p.5-20|共16页
作者
Jarosław Pykacz;
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正文语种 eng
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关键词
quantum logic; many; valued logic; Łukasiewicz logic;

机译：量子逻辑;许多有价值的逻辑Łukasiewicz逻辑;

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专利

1. Unification of Two Approaches to Quantum Logic: Every Birkhoff - von Neumann Quantum Logic is a Partial Infinite-Valued ?ukasiewicz Logic [J] . Pykacz J. Studia Logica . 2010,第1a2期

机译：两种量子逻辑方法的统一：每个Birkhoff-von Neumann量子逻辑都是部分无穷大的？ukasiewicz逻辑
2. QUANTUM LOGIC AS PARTIAL INFINITE-VALUED LUKASIEWICZ LOGIC [J] . Pykacz J. International Journal of Theoretical Physics: A Journal of Original Research and Reviews in Theoretical Physics and Related Mathematics, Dedicated to the Unification of Physics . 1995,第8期

机译：量子逻辑作为部分无限值LUKASIEWICZ逻辑
3. Emergence of fuzzy preferences for risk in a Birkhoff-von Neumann logics environment [J] . Emmanuel Haven Fuzzy sets and systems . 2005,第1期

机译：Birkhoff-von Neumann逻辑环境中风险的模糊偏好的出现
4. A Quantum Interpretation of Bunched Logic Quantum Separation Logic [C] . Li Zhou, Gilles Barthe, Justin Hsu, Annual ACM/IEEE Symposium on Logic in Computer Science . 2021

机译：束缚逻辑和量子分离逻辑的量子解释
5. QUANTUM LOGIC, QUANTUM PROBABILITY, AND QUANTUM MEASUREMENT: A PHILOSOPHICAL PERSPECTIVE ON THE QUANTUM THEORY. [D] . NILSON, DONALD RICHARD. 1972

机译：量子逻辑，量子概率和量子测量：量子理论的哲学视角。
6. Unification in Łukasiewicz Logic with a Finite Number of Variables [O] . Marco Abbadini, Federica Di Stefano, Luca Spada -1

机译：有限变量在Łukasiewicz逻辑中的统一
7. Von Neumann Quantum Logic vs. Classical von Neumann Architecture? [O] . Vlasov, Alexander Yu. 2000

机译：冯诺依曼量子逻辑与古典冯诺依曼建筑？
8. Quantum Approaches to Logic Circuit Synthesis and Testing [R] . Hayes, J. P. , Markov, I. L. 2006

机译：逻辑电路综合与测试的量子方法

Unification of Two Approaches to Quantum Logic: Every Birkhoff – von Neumann Quantum Logic is a Partial Infinite-Valued Łukasiewicz Logic

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