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Classical computers, which we use on a daily basis, are built upon the concept of digital logic and bits. Thus our classical logic is a completion of the quantum logic QL. More specifically, in quantum mechanics each probability-bearing proposition of the form “the value of physical quantity $$A$$ lies in the range $$B$$” is represented by a projection operator on a Hilbert space $$\mathbf{H}$$. Classical computing vs quantum computing By Joseph Fernandez July 19, 2018. These mathematical studies, have shown that the quantum logical implication and conjunc-tion can be interpreted as their classical equivalents, while this is not the case for the quantum logical disjunction and negation. and quantum deductive logic and classical deductive logic Just as Boolean logic provides the basis upon which modern classical computing logic is formed, clearly expressed quantum logic is now required in order to fully utilize quantum computing power. logic so de ned deductive quantum logic.2 Classical logic is deductive in the same sense. Mathematically, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic. Jauch, Piron, Greechie, and Gudder above assumed the conditional|from now on we will call it implication|to be de ned as a !0 b = a0 [ b (see Section 2 for notation). The existence of a quantum logic is shown to be related to the general context-dependent character of statements and this claim is illustrated by examples taken from outside the domain of physics. Soundness and completeness of both quantum and classical logics have been proved for novel lattice models that are not orthomodular and therefore cannot be distributive either - as opposed to the standard lattice models that are orthomodular and distributive for the respective logics. We also show that there is one common nonorthomodular lattice that is a model of both quantum and classical logic. identify the structural differences between quantum logic and classical logic (von Neu-mann 1932; Birkhoff and von Neumann 1936; Beltrametti and Cassinelli 1981). It is shown that quantum logic is a logic in the very same way in which classical logic is a logic. The logic internal to the meta-context-language is a non-classical logic; the logic of quantum event language is or could be classical. The second part of the project includes a visual demonstration of the classical and quantum particle (spin 1/2) movement over the detectors. In the early seventies, a number of results and a number of predecessors to deductive quantum logics were formulated. The project simulates Quantum logic versus Classical logic using HMI-PLC.The first part of the project demonstrates graphically the difference between the way Classical gates work and the way Quantum gates work. In particular, we prove that both classical logic and quantum logic are sound and complete with respect to each of these lattices. In other words, we refute Birkhoff and von Neumann's classic thesis that the logic (the formal character) of Quantum Mechanics would be non-classical as well as Putnam's thesis that quantum logic (of his kind) would be the correct logic for propositional inference in general. A bit is simply an idea, or an object, which can take on one of two distinct values, typically labeled 0 or 1. 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