Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK.
Philos Trans A Math Phys Eng Sci. 2019 Nov 4;377(2157):20190036. doi: 10.1098/rsta.2019.0036. Epub 2019 Sep 16.
We establish a strong link between two apparently unrelated topics: the study of conflicting information in the formal framework of valuation algebras, and the phenomena of non-locality and contextuality. In particular, we show that these peculiar features of quantum theory are mathematically equivalent to a general notion of between information sources. This result vastly generalizes previously observed connections between contextuality, relat- ional databases, constraint satisfaction problems and logical paradoxes, and gives further proof that contextual behaviour is not a phenomenon limited to quantum physics, but pervades various domains of mathematics and computer science. The connection allows to translate theorems, methods and algorithms from one field to the other, and paves the way for the application of generic inference algorithms to study contextuality. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.
我们在形式估值代数框架内对冲突信息的研究，以及非定域性和语境相关性的现象之间建立了牢固的联系。具体来说，我们证明了量子理论的这些奇特特征在数学上与信息源之间的一般概念等价。这个结果极大地推广了先前观察到的语境相关性、关系数据库、约束满足问题和逻辑悖论之间的联系，并进一步证明了语境行为不仅是一种局限于量子物理学的现象，而是贯穿了数学和计算机科学的各个领域。这种联系允许将一个领域的定理、方法和算法转换到另一个领域，并为应用通用推理算法来研究语境相关性铺平了道路。本文是“量子力学及其他领域的语境相关性和概率”主题特刊的一部分。
