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Geometric viewpoint on the quantization of a fuzzy logic
International Journal of Geometric Methods in Modern Physics ( IF 1.8 ) Pub Date : 2020-09-10 , DOI: 10.1142/s0219887820502011
Davide Pastorello 1, 2
Affiliation  

Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel [Formula: see text]-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations. Considering the geometric formulation of quantum mechanics we give a description of quantum propositions in terms of fuzzy events in a complex projective space equipped with Kähler structure (the quantum phase space) obtaining a quantized version of a fuzzy logic by deformation of the product [Formula: see text]-norm.

中文翻译:

模糊逻辑量化的几何观点

在哈密顿框架内,关于经典物理系统的命题在辛流形(相空间)的 Borel [公式:见正文]-代数中描述,其中逻辑连接词是标准集合操作。考虑到量子力学的几何公式​​,我们在配备 Kähler 结构(量子相空间)的复杂射影空间中根据模糊事件来描述量子命题,通过乘积的变形获得模糊逻辑的量化版本 [公式:见正文]-规范。
更新日期:2020-09-10
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