Application of Shannon Entropy in the Construction of a Paraconsistent Model of the Atom

In this paper, we present a model of the atom that is based on a nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The proposed model is constructed with an extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v), which is associated with an interlaced lattice of four vertices. We use the logarithmic function of the Shannon entropy H(s) to construct the paraconsistent equations and thus adopt a probabilistic model for representations in quantum physics. Through analyses of the interlaced lattice, comparative values are obtained for some of the phenomena and effects of quantum mechanics, such as superposition of states, wave functions, and equations that determine the energy levels of the atomic shells of an atom. At the end of this article, we use the hydrogen atom as a basis for the representation of the PAL2v model, where the values of the energy levels in six orbital shells are obtained. As an example, we present a possible method of applying the PAL2v model to the use of Raman spectroscopy signals in the detection of lubricating mineral oil quality.