量化概率逻辑的初等不变量

IF 0.5 4区数学 Q3 MATHEMATICS Doklady Mathematics Pub Date : 2023-08-30 DOI:10.1134/S1064562423700667

S. O. Speranski

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引用次数: 0

摘要

设QPL为[8]中提出的二排序概率语言，它通过在事件上添加量词，扩展了[3]第6节中描述的众所周知的“多项式”语言。我们证明了所有的无原子空间都有相同的量子物理理论，并且这个理论是可确定的。此外，我们还引入了QPL的初等不变量的概念，并利用它获得了一些有趣的概率理论的精确复杂度上界。

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Elementary Invariants for Quantified Probability Logic

Let QPL be the two-sorted probabilistic language proposed in [8], which expands the well-known ‘polynomial’ language described in [3], Section 6, by adding quantifiers over events. We show that all atomless spaces have the same QPL-theory, and this theory is decidable. Also we introduce the notion of elementary invariant for QPL and use it for obtaining exact complexity upper bounds for some interesting probabilistic theories.

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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.