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

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.

Paraconsistent mathematics, also called Inconsistent Mathematics, is considered as the study of common mathematical objects, such as sets, numbers and functions, where some contradictions are allowed. Within certain conditions, Paraconsistent logic (PL), which is a non-classical Logic, presents as main property tolerance contradiction in its fundamentals without that the conclusions are invalidated. The PL in its structural form, which uses two annotation values-PAL2v, can be used to substantiate a Differential Calculus with Paraconsistent derivative of first and second order. We introduce here the Paraconsistent Partial Differential Equation (PPDE) aligned with processes of numerical methods for an example application in analysis with Explicit solution of temperature distribution in one-dimensional way. To obtain the results was used an analogy of application of PPDE with the law of heat conduction of Fourier, considering the same mathematical procedures of finite differences.

Part I of this study proved that the Paraconsistent Annotated Logic using two values (PAL2v), known as the Paraquantum Logic (PQL), can represent the quantum by a model comprising two wave functions obtained from interference phenomena in the 2W (two-wave) region of Young’s experiment (double slit). With this model represented in one spatial dimension, we studied in the Lattice of the PQL, with their values represented in the set of complex numbers, the state vector of unitary module and its correspondence with the two wave functions. Based on these considerations, we applied the PQL model for obtaining Paraquantum logical states ψ related to energy levels, following the principles of the wave theory through SchrOdinger’s equation. We also applied the probability theory and Bonferroni’s inequality for demonstrating that quantum wave functions, represented by evidence degrees, are probabilistic functions studied in the PQL Lattice, confirming that the final Paraquantum Logic Model is well suited to studies involving aspects of the wave-particle theory. This approach of quantum theory using Paraconsistent logic allows the interpretation of various phenomena of Quantum Mechanics, so it is quite promising for creating efficient models in the physical analysis and quantum computing processes.

Paraconsistent logic (PL) is a non-classical logic that accepts contradiction in its foundations. It can be represented in the form of paraconsistent annotated logic with annotation of two values (PAL2v). When used to model quantum phenomena, PAL2v is called paraquantum logic (PQL). In this work, the concept of PQL is applied to create a logical model presenting the fundamental principles of quantum mechanics that support particle-wave theory. This study uses the well-known Young’s double-slit experiment, wherein quantum phenomena appear when a monochromatic light beam passes through the two slits. We focused on a reference point located between the slits, where we observed the effects of two types of wave interferences in a region defined as a two-wave region (2W region). Considering that the effect in this 2W region is very similar to that studied by Huygens, we adopt a paraquantum logical model in which a particle (or quantum) is represented by two wave functions. The two wave functions result in four State Vectors (Ket, Bra,,) in the PQL Lattice that express the symmetry and the entanglement of Quantum Mechanics. The constructed model adapts well to the quantum phenomena, is strongly consistent, and can be considered as an innovative form of analysis in the field of quantum mechanics. Based on this model, we present in two parts (Part I and Part II) the comparative analysis of values found in SchrOdinger’s equation and probabilistic models of wave-particle theory using Bonferroni inequality.

Analysis of the Raman data to obtain results in discrimination models is usually done with multivariate statistics based on principal component analysis (PCA). In this work, we present a technique based on a non-classical logic called paraconsistent logic (PL). The aim of this work is to use computational procedures capable of generating efficient expert systems to discriminate cutaneous tissue samples obtained by Raman spectroscopy. First, a set of algorithms originating from PL is presented, and then its application in discrimination analyses is described; the discrimination analysis was conducted using a database of skin tissue samples obtained ex vivo by Raman spectroscopy of spectrum range of 400–1800 cm−1 wavelengths. Data processing, pattern creation, and comparisons were performed using the set of paraconsistent algorithms (SPA-PAL2v). The total number of samples was divided into four histopathological groups, with 115 spectra of basal cell carcinoma (BCC), 21 spectra of squamous cell carcinoma (SCC), 57 spectra of actinic keratosis (AK), and 30 normal skin (NO) spectra. An arrangement type was created for this study, and the samples were randomly selected and analyzed, and the NO group was compared with the group of non-melanoma cancer lesions (BCC + SCC) and the AK tumor lesion. Two analyses were performed. The first (SPA-PAL2v) Mode 1 (no cross-validation) achieved 76% of hits, and the second (SPA-PAL2v) Mode 2 (with cross-validation) achieved 75.78% of hits. These results were compared with discrimination using PCA statistical methods (PCA/DA) and presented superior percentages of hits, which proves the robustness of the SPA-PAL2v, confirming its potential for Raman spectrum data analysis.

Paraquantum Logics (PQL) has its origins in the fundamental concepts of the Paraconsistent Annotated Logics (PAL) whose main feature is to be capable of treating contradictory information. Based on a class of logics called Paraconsistent Logics with annotations of two values (PAL2v), PQL performs a logical treatment on signals obtained by measurements on physical quantities which are considered Observable Variables in the physical world. In the process of application of the PQL the obtained values are transformed in Evidence Degrees and represented on a Lattice of four Ver- tices where special equations transform these degrees into Paraquantum logical states ψ which propagate. The propagation of Paraquantum logical states provides us with results which can be interpreted and modeled through phenomena studied in physics. Using the paraquantum equations, we investigate the effects of balancing of Energies and the quantization and transience properties of the Paraquantum Logical Model in real Physical Systems. As a demonstration of the usage of the paraquantum equations we perform a numerical comparative study that applies the PQL to the Bohr’s model to find the energy levels of the Hydrogen atom. It is verified that the values of energy in each level of the Paraquantum logical model of the Hydrogen atom are close to the values found by the conventional way. The results through the Paraquantum Logic allow considering other important properties of the atom, as the forecast of number of electrons in each layer.

Paraquantum Logic (P QL ) has its origins in the fundamental concepts of the Paraconsistent Annotated Logic (PAL) whose main feature is to be capable of treating contradictory information. In this work we presented a study of application of the P QL in resolution of phenomena of physical systems that involves the interactions between physical bodies or particles. Initially is considered that each particle or physical body that is in the physical world has a representative Lattice in the Paraquantum world. From this consideration is made a study of the phenomena of Paraquantum Entanglement modeling the interaction between particles based in fundamental concepts of the Paraquantum Logic. The mathematical relationships of representative Lattices of the Paraquantum Logic originate models with values that are identified with some physical constants. In this work these paraquantum values are identified with the Universal constant of Gravity, proposed by Newton, and the constant K, that relates the Interaction Force in charged particles in the Coulomb’s Law. The results showed that the Paraquantum Logical Model elaborated starting from the fundamental concepts of the Paraquantum Logic (P QL ) is adequate to support theories based in a Paraquantum Universe built by an infinite amount of Lattices and forming a Paraquantum net of infinite dimensions.

In this work, we present a Simulator Program that identifies the topologies and supports operation staff in decision-making about loads reassignments and changes in electric network, offering a selection of the best settings. Facing a contingency situation or action of relocation of electrical system of subtransmission lines, the Simulator considers the current state and uses special algorithms that detect the current network topology, interprets results and presents for operation the possible different maneuvers with their respective degrees of reliability. For these actions the software Simulator elaborates the states investigation of circuit breakers and electric keys, analysis of load flow, makes risk prediction and the mathematical analysis of remote sensing values. The software Simulator uses in some of his actions, special algorithms that are based on Paraconsistent Annotated Logic (PAL), which is a non-classical logic whose main property is to accept contradiction in their fundamentals. These algorithms based on PAL offer greater speed of processing and allows the Paraconsistent Simulator of topologies (ParaSimTop) to be implemented in real time.

In this paper, we present an application of the Paraconsistent Artificial Neural Network (PANnet) in a Statistical Process Control to trigger alarms in an electrical power System. The PANnet is based on Paraconsistent Annotated Logic (PAL) which is a non-classical logic with properties of accepting contradictions in their fundamentals. In this work, we make a joint application technique of Paraconsistent Annotated logic, in the form of PANnet, with the concepts of Statistical Process Control (SPC). The Statistical Process Control Paraconsistent (SCP-PAL) is used in this paper to make a dynamic monitoring of the conditions of the electrical voltage in an electrical power system. To test and validate the functioning of SPC-PAL Controller we use data obtained by random computational processes and we also use a database with actual values generated by a power electrical System of a company installed in Brazil. The SPC-PAL Controller, due to the use of the algorithms of PAL in its construction, has some features that does afford optimized electrical voltage monitoring. The result of the analysis made with the SPC-PAL Controller provides three types of alarms: 1) rapid Variation in the voltage; 2) Imbalance of Mean in the Voltage data; 3) High dispersion index in the voltage data. Based on these three types of alarms we can obtain a better understanding about the operating state of the electrical power system. In the various tests performed, the SPC-PAL Controller presented a good performance and detected changes in Mean and in the variation of tension, as well as sudden changes in voltage data.

This chapter presents the development of a Expert System which was elaborated based on the Fundamentals of Paraconsistent Annotated Logic and aimed to help in the process of detection of physiological stress in organisms exposed to water pollution. The Paraconsistent Logic is a non-classical logic present as their main characteristics the acceptance of the contradiction in their structure. It is presented in this study the algorithms extracted from a type of Paraconsistent Logic nominated Paraconsistent Annotated Logic with annotation of two values PAL2v that are capable of simulating the applied methodology in Biology known as a neutral red retention assay. This method of biomarkers prepared with specific procedures has the goal of finding rates of exposure to marine pollution through the manipulation and study of cells from mussels. It was built a configuration of Paraconsistent Artificial Neural Network (PANN) composed of algorithms based on the principals of Paraconsistent Logic to compose the Expert System with the goal of simulating the biological method and help in the presentation of the cellular response. The process of analysis elaborated by the software consists of making a comparison with pre-established patterns through the Paraconsistent Network by biochemical/biological processes consolidated in the biology area and defined in the scope on the mussels cells’ measures that presented determined behavior and biochemical reactions, as it is the biomarker of exposure and effect of marine pollution in the site of the samples collection. With this new approach of results, besides complete, they are presented as being more efficient by decreasing the points of uncertainty given by simple human observation. This way this work opens new fields for research of application of Artificial Intelligence techniques in the analysis and monitoring of the Marine Pollution.

This paper shows the results of the sensing system which was designed for the autonomous mobile robot Emmy III. The proposed Sensing System has as its mean part the Paraconsistent Neural Network. This artificial neural network is based on the Paraconsistent Evidential Logics — Et. The objective of the Sensing System is to inform the other robot components about the obstacle position. The reached results have been satisfactory.

All over the world cardiovascular diseases are responsible for a great number of clinical problems that result in death. Arterial Hypertension is considered one of the main agents of such diseases and, for that reason, the correct detection of Hypertension symptoms is very important for the medical area. In this work we use the Paraconsistent Logic (PL) as a method of treatment of uncertainties to help health professionals that act in this medical area. With base in the concepts of the Paraconsistent Logic we created a Expert System for the help in the analysis and diagnosis in cardiovascular diseases. This computational system is called “ParaHyper Analyzer” and it uses Algorithms of the Paraconsistent Logic, a non-classical kind of logic, for the treatment of contradictory information. The algorithms are obtained through the interpretation of the representative Lattice of Paraconsistent Annotated Logic with annotation of two values (PAL2v), where the certainty degree (DC) and the contradiction degree (Dct) are calculated, according to the logical methodology. The PAL2v algorithms are called Paraconsistent Analysis Nodes (PAN). The PAN allows the analysis of propositions which are related to changes in the blood pressure, so that the patient can be classified in a certain risk group. The ParaHyper Analyzer studies this information and presents a result which shows the possibility of developing a serious cardiovascular disease.

This work presents some improvements regarding to the autonomous mobile robot Emmy based on Paraconsistent Annotated Evidential Logic Eτ. A discussion on navigation system is presented.

This paper shows the results of a sensing system for an autonomous mobile robot. The sensing system is based on the paraconsistent neural network. The type of artificial neural network used in this work is based on the paraconsistent evidential logic (Eτ). The objective of the sensing system is to inform the other robot components the obstacle position. The reached results have been satisfactory.

Vários métodos estatísticos aplicados à medicina diagnóstica sofreram, nas últimas décadas, enormes avanços. Grande parte destes métodos está voltada ao problema de classificar indivíduos em grupos, sendo que os testes diagnósticos ligados a técnicas de Inteligência Artificial compõem nossa principal aplicação desse trabalho. Estes testes estatísticos são descritos como métodos teoricamente capazes de indicar a presença ou a ausência de uma determinada doença, com certa chance de erro. A quantificação destas chances de erro que é, basicamente, o objetivo destes métodos tem servido a inúmeras aplicações e nesse trabalho é utilizada como fonte de evidências para os procedimentos de análises estruturados em Lógica Paraconsistente. Como a Lógica Paraconsistente é uma lógica não-clássica que aceita contradição em sua estrutura sem invalidar as conclusões, e utiliza em suas análises valores evidenciais, aplicamos aqui os conceitos fundamentais de um tipo de Lógica Paraconsistente denominada de Lógica Paraconsistente Anotada com anotação de dois valores LPA2v. Através dos procedimentos estatísticos e os fundamentos da LPA2v o presente estudo objetiva descrever a situação em que o teste produz uma resposta que não é descrita simplesmente como positivo ou negativo, mas por um resultado que pode ser expresso por uma variável categórica ordinal ou por uma variável contínua que pode ser considerada como grau de evidência. Esse processo é realizado utilizando uma dedução lógica que usa os conceitos da Probabilidade Pragmática na qual se pode efetuar uma ligação entre a teoria probabilística de Bayes e os métodos de aplicação da Lógica Paraconsistente Anotada com dois valores LPA2v. Dessa junção surgiram neste trabalho algoritmos Paraconsistentes que descrevem esse processo. Denominamos o processo de adaptação da Teoria de Bayes para a Lógica Paraconsistente de ParaBayes. Para demonstrar os procedimentos que utilizam os conceitos fundamentais da LPA2v em dados probabilísticos foram extraídos valores evidenciais de um banco de dados que se refere à submissão de um conjunto de casos, contendo uma série de evidências e o diagnóstico de Diabetes, em uma comunidade de índias PIMA. São utilizadas no banco de dados índias PIMA as técnicas dos métodos estatísticos e de raciocínio probabilístico de Bayes para levantamento de dados que foram interpretados e modelados como Graus de Evidência capazes de serem analisados pelos Algoritmos da LPA2v. Neste estudo verifica-se que a extração dos Graus de Evidência não invalida as técnicas estatísticas já estabelecidas, mas confere através da LPA2v novas formas de interpretação baseadas nos resultados e produzindo meios que facilitam o tratamento dos dados por ferramentas computacionais elevando o grau de confiança dos diagnósticos. Uma das observações importantes é que o método LPA2v/Bayes proposto utilizado para extrair evidências é capaz de evitar possíveis distorções no formato da curva que possam advir da seleção inadequada de casos de teste. Os resultados obtidos sugerem que em situações nas quais se tenha uma grande quantidade de casos em que as incertezas exijam métodos estatísticos para formar diagnóstico, esta seja uma boa técnica para se adotar em sistemas de apoio a decisão médica. Several statistical methods applied to the medicine diagnostic suffered, in the last decades, enormous progresses. Great part of these methods come back to the problem from classifying individuals in groups. Tests that use techniques of Artificial Intelligence compose our main main focus. Statistical tests are described as methods capable to indicate the presence or the absence of a certain disease, with a certain chance of error. The quantification of these error chances that is, basically, the objective of these methods has served to countless applications. In this work it is used as source of evidence for the procedures of analysis structured through Paraconsistent Logic. As Paraconsistent Logic is a non-classic logic that accepts contradiction in its structure without invalidating the conclusions and uses in its analysis values attributed to evidences, we applied the fundamental concepts of a type of Logic denominated Paraconsistent Logic Annotated with two values LPA2v. Through the statistical procedures and the foundations of LPA2v the present study aims at describing the situation where the test produces an answer that is not simply described as \"positive\" or \"negative\", but can be expressed by an ordinal variable or by a continuous variable that can be considered as an evidence degree. That process is obtained using a logical deduction that uses the concepts of the Pragmatic Probability where it can make a connection between the probabilistic theory of Bayes and the methods of Paraconsistent Logic, Annotated with two values, LPA2v. Out of that junction Paraconsistent algorithms appeared in this work that describe the whole process. We denominated the process of adaptation of the Theory of Bayes to Paraconsistent Logic of ParaBayes. To demonstrate the procedures that use the fundamental concepts of LPA2v evidence values were extracted from a database comprising a series of evidences and the diagnosis of Diabetes, in a community of PIMA Indians. The PIMA Indian database was a test-bed field for the techniques of the statistical methods and of reasoning probabilistic of Bayes for rising of data that were interpreted and modeled as Degrees of Evidence capable of being analyzed by the Algorithms of LPA2v. In this study it is verified that the extraction of the Degrees of Evidence doesn\'t invalidate the statistical techniques established, but it allows for new forms of interpretations based on the results and producing means that facilitate the treatment of the data, elevating the trust in the diagnostic. One of the important observations is that the proposed method LPA2v/Bayes used to extract evidence is capable to avoid possible distortions in the format of the curve that is usually the result of inadequate selection of test cases. Results suggest that in situations where a great amount of cases have uncertainties this is a good technique to adopt in medical decision support systems.

O reconhecimento de padrões por computador é uma das mais importantes ferramentas da Inteligência Artificial presente em inúmeras áreas do conhecimento com aplicações em diversos setores, incluindo o reconhecimento de caracteres. O objetivo da dissertação se concentra na investigação de um processo computacional automatizado - Sistema Computacional Paraconsistente - capaz de reconhecer Caracteres Numéricos Manuscritos e Caracteres Magnéticos Codificados em 7 Barras utilizados em cheques bancários brasileiros, fornecendo uma fundamentação técnica para reconhecer documentos e imagens digitalizadas e, também, sinais biológicos. Embora haja vários estudos em reconhecimento de caracteres, optou-se pelo estudo desse tema devido à sua intrínseca importância e constante desenvolvimento, além de possibilitar adaptações para fazer o reconhecimento de diferentes tipos de sinais como, por exemplo, sinais biológicos. A metodologia adotada para essa tarefa se baseia nas Redes Neurais Artificiais Paraconsistentes por se tratar de uma ferramenta com capacidade de trabalhar com dados imprecisos, inconsistentes e paracompletos sem o perigo de trivialização. O processo de reconhecimento desse sistema é realizado a partir de algumas características do caractere previamente selecionadas com base em algumas técnicas do Grafismo e realiza-se a análise dessas características bem como o reconhecimento do caractere através das Redes Neurais Artificiais Paraconsistentes O sistema foi construído para reconhecer caracteres numéricos com um padrão previamente definido, onde adotou-se os Caracteres Magnéticos Codificados em 7 Barras utilizados em cheques bancários e, posteriormente, o sistema foi aperfeiçoado para fazer o reconhecimento de Caracteres Numéricos Manuscritos. Para a validação do estudo proposto apresentou-se dados reais, a saber, lotes de cheques e caracteres numéricos manuscritos digitalizados onde o sistema apresentou 97,85% de acertos para os Caracteres Magnéticos Codificados em 7 Barras e 91,62% de acertos para Caracteres Numéricos Manuscritos. O resultado obtido demonstra que o sistema é robusto o suficiente e pode servir de estudo para a análise de sinais em áreas correlatas com nível de precisão semelhante Computer pattern recognition is one of the most important Artificial Intelligence tools present in numerous knowledge areas with applications in several themes, including the character recognition. The aim of this dissertation is the investigation of an automated computational process - Paraconsistent Computational System - able to recognize Handwritten Numeric Characters and Magnetic Ink Character Recognition used on Brazilian bank checks furnishing a technical basis to recognize digital documents, digital images and biological signals. Although there are several studies on character recognition, it was chosen to study this theme due to its intrinsic importance and constant improvement, besides enabling adjustments to the recognition of different kinds of signals such as, biological signals. The methodology employed for the task is based on Paraconsistent Artificial Neural Networks for being a tool with the ability to work with imprecise, inconsistent and paracomplete data without trivialization. The recognition process of this system is performed from some previously selected character features based on some Graphics techniques and, it performs the analysis of these features as well as the character recognition are performed through the Paraconsistent Artificial Neural Networks. The system was built to recognize numeric characters with a previously defined pattern where it was chosen the Magnetic Ink Character Recognition used on Brazilian bank checks and then the system was improved to recognize handwritten numeric characters. It was presented real data as checks\' batches and scanned handwritten numeric characters to validate the proposed study and the system reached 97.85% hits for Magnetic Ink Character Recognition and 91.62% hits for Handwritten Numeric Characters. The obtained result demonstrates that the system is robust enough for signal analysis study in correlated areas with similar precision level