论文标题
关于模糊逻辑量化的几何观点
Geometric viewpoint on the quantization of a fuzzy logic
论文作者
论文摘要
在哈密顿式框架内，有关经典物理系统的命题在逻辑歧管（相位空间）的Borelσ-代数中描述，其中逻辑连接是标准设置操作。考虑到量子力学的几何表述，我们对量子命题的描述描述了一个复杂的投影空间中的模糊事件，该空间配备了Kähler结构（量子相空间），从而通过产物T-Norm的变形获得了模糊逻辑的量化版本。
Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel σ-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 t-norm.
