Geometric viewpoint on the quantization of a fuzzy logic

• URL: http://arxiv.org/abs/2004.03395v1
• Date: Mon, 6 Apr 2020 13:37:02 GMT
• Title: Geometric viewpoint on the quantization of a fuzzy logic
• Authors: Davide Pastorello
• Abstract summary: We give a description of quantum propositions in terms of fuzzy events in a complex projective space equipped with K"ahler structure (the quantum phase space) We obtain a quantized version of a fuzzy logic by deformation of the product t-norm.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel {\sigma}-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 K\"ahler structure (the quantum phase space) obtaining a quantized version of a fuzzy logic by deformation of the product t-norm.

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