Abstract
In this work, we make a representation of non-relativistic quantum theory based on foundations of paraconsistent annotated logic (PAL), a propositional and evidential logic with an associated lattice FOUR. We use the PAL version with annotation of two values (PAL2v), named paraquantum logic (PQL), where the evidence signals are normalized values and the intensities of the inconsistencies are represented by degrees of contradiction. Quantum mechanics is represented through mapping on the interlaced bilattices where this logical formalization allows annotation of two values in the format of degrees of evidence of probability. The Bernoulli probability distribution is used to establish probabilistic logical states that identify the superposition of states and quantum entanglement with the equations and determine the state vectors located inside the interlaced Bilattice. In the proposed logical probabilistic paraquantum logic model (pPQL Model), we introduce the operation of logical conflation into interlaced bilattice. We verify that in the pPQL Model, the operation of logical conflation is responsible for providing a suitable model for various phenomena of quantum mechanics, mainly the quantum entanglement. The results obtained from the entanglement equations demonstrate the formalization and completeness of paraquantum logic that allows for interpretations of similar phenomena of quantum mechanics, including EPR paradox and the wave-particle theory.
Highlights
Studying the effects of undulatory theory of light, researchers found that experiments in modern physics dealing with quantum mechanics lead to results that are incompatible with classical physics
With the pPQL-Model associated at interlaced bilattice FOUR, a representation was built that enables good visualization of the superposed paraquantum logical states behavior
We presented a logical model that combines non-relativistic quantum mechanics with probabilistic theory of the Bernoulli distribution, bilattices theory, and foundations of paraconsistent logic
Summary
Studying the effects of undulatory theory of light, researchers found that experiments in modern physics dealing with quantum mechanics lead to results that are incompatible with classical physics This contradiction between classical theory and modern experimental research requires a fundamental modification of basic physical concepts and laws so that they can apply to atomic phenomena [1] [2] [3] [4]. From these observations, investigations have been conducted to find the foundations of a new logic more suitable for creating equations and models for quantum mechanics [5]. We highlight those [13] [14] [15] where the authors use non-classical logics such as fuzzy and paraconsistent logic to create the formalization of a quantum logic
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