L. A. Zadeh, “Causality Is Undefinable—Toward a Theory of Hierarchical Definability,” Proceedings of FUZZIEEE, Melbourne, 2-5 December 2001, pp. 67-68

has been cited by the following article:

• TITLE: Bipolar Quantum Logic Gates and Quantum Cellular Combinatorics—A Logical Extension to Quantum Entanglement

  AUTHORS: Wen-Ran Zhang

  KEYWORDS: Bipolar Causal Sets; Logically Definable Causality; Basis State Quantum Entanglement; Generic and Composite Entanglement; Bipolar Equilibrium; Bipolar Quantum Logic Gates; Quantum Cellular Combinatorics

  JOURNAL NAME: Journal of Quantum Information Science, Vol.3 No.2, June 14, 2013

  ABSTRACT: Based on bipolar dynamic logic (BDL) and bipolar quantum linear algebra (BQLA) this work introduces bipolar quantum logic gates and quantum cellular combinatorics with a logical interpretation to quantum entanglement. It is shown that: 1) BDL leads to logically definable causality and generic particle-antiparticle bipolar quantum entanglement; 2) BQLA makes composite atom-atom bipolar quantum entanglement reachable. Certain logical equivalence is identified between the new interpretation and established ones. A logical reversibility theorem is presented for ubiquitous quantum computing. Physical reversibility is briefly discussed. It is shown that a bipolar matrix can be either a modular generalization of a quantum logic gate matrix or a cellular connectivity matrix. Based on this observation, a scalable graph theory of quantum cellular combinatorics is proposed. It is contended that this work constitutes an equilibrium-based logical extension to Bohr’s particle-wave complementarity principle, Bohm’s wave function and Bell’s theorem. In the meantime, it is suggested that the result may also serve as a resolution, rather than a falsification, to the EPR paradox and, therefore, a equilibrium-based logical unification of local realism and quantum non-locality.