Um estudo sobre as origens da Lógica Matemáitca

The present study has as objective to explaining about the origins of the mathematical logic. This has its beginning attributed to the autodidactic English mathematician George Boole (1815-1864), especially because his books The Mathematical Analysis of Logic (1847) and An Investigation of the Laws of Thought (1854) are recognized as the inaugural works of the referred branch. However, surprisingly, in the same time another mathematician called Augutus of Morgan (1806-1871) it also published a book, entitled Formal Logic (1847), in defense of the mathematic logic. Even so, times later on this same century, another work named Elements of Logic (1875) it appeared evidencing the Aristotelian logic with Richard Whately (1787-1863), considered the better Aristotelian logical of that time. This way, our research, permeated by the history of the mathematics, it intends to study the logic produced by these submerged personages in the golden age of the mathematics (19th century) to we compare the valid systems in referred period and we clarify the origins of the mathematical logic. For that we looked for to delineate the panorama historical wrapper of this study. We described, shortly, biographical considerations about these three representatives of the logic of the 19th century formed an alliance with the exhibition of their point of view as for the logic to the light of the works mentioned above. In this sense, we aspirated to present considerations about what effective Aristotelian´s logic existed in the period of Boole and De Morgan comparing it with the new emerging logic (the mathematical logic). Besides of this, before the textual analysis of the works mentioned above, we still looked for to confront the systems of Boole and De Morgan for we arrive to the reason because the Boole´s system was considered better and more efficient. Separate of this preponderance we longed to study the flaws verified in the logical system of Boole front to their contemporaries' production, verifying, for example, if they repeated or not. We concluded that the origins of the mathematical logic is in the works of logic of George Boole, because, in them, has the presentation of a new logic, matematizada for the laws of the thought similar to the one of the arithmetic, while De Morgan, in your work, expand the Aristotelian logic, but it was still arrested to her

Uma reavaliação do pensamento lógico de George Boole à luz da história da matemática

The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics

Redes sociais e a lógica do desvio comportamental em relação às normas de trabalho

This paper aim to check a hypothesis that assumes several behaviors related to social work norm´s obeying as a phenomenon that can be explained by actor´s social network structure and the rational choice processes related to the social norm inside that network, principally the payoff´s analysis received by the closest actors, or neighbors, at a social situation. Taking the sociological paradigm of rational action theory as a basis, the focus is on a debate about the logic of social norms, from Émile Durkheim´s method to Jon Elster´s theory, but also including social network analysis´s variables according to Robert Hanneman; and also Vilfredo Pareto´s constants related to human sociability, at the aim to detect elements that can help the scholars to develop an agent based model which could explain the sociological problem of deviance by a better way than the common sense´s view about morality and ethics at a social work environment

Uma visita ao universo matemático de Lewis Carrol e o (re)encontro com sua lógica do nonsense

Notable mathematics teacher, Lewis Carroll, pseudonym of Charles Lutwidge Dodgson (1832-1898), made the mixture of mathematics with literature a ludic environment for learning that discipline. Author of Alice s Adventures In Wonderland and its sequel Alice Through The Looking Glass, he eventually created a real and complex universe which uses what we call the logic of the nonsense as an element to motivate the development of mathematical thinking of the reader, taking it as well, learn by establishing a link between the concrete (mathematics) and the imaginary (their universe). In order to investigate and discuss the educational potential of their works and state some elements that can contribute to a decentralized math education from the traditional method of following the models and decorate formulas, we visited his works based on the studies of archeology of knowledge (FOUCAULT, 2007), the rational thought and symbolic thinking (VERGANI, 2003) and about the importance of stories and narratives to the development of human cognition (FARIAS, 2006). Through a descriptive, analytical study, we used the literary construction and presented part of our study in form of a mathematical novel, to give the mathematical school a particular charm, without depriving it of its basics properties as discipline and content. Our study showed how the works of Carroll have a strong didactic element that can deploy in various activities of study and teaching for mathematics classes

O processo avaliativo institucional de desempenho do sistema público municipal de Teresina-PI (2001 a 2005): entre a lógica da excelência e a lógica da aprendizagem

This work focalize the institutional and educational evaluation, aiming to investigate the Municipal System Institutional Evaluation Performance of Teresina City Piauí (2001-2005), and to reflect about Institutional System Performance and its contribution to compose a new learning evaluation practice. In this sense, classifies elements about the evaluation practice in two Elementary Education municipal public schools, involving Education Municipal Bureau technicians as managers, pedagogues, teachers and students. Based on the ethnographic studies principles in the educational area, the work employs investigative procedures like document analysis, interviews with groups and individuals and also participator s comments. Intending to comprehend the complexity produced by the institutional and education evaluation processes, the wok reveals the Institutional Evaluation legal and educational political basis and the several positions assumed by the Learning Evaluation, as a classification tool or as a learning enhancement. This work points, as results, to a evaluation culture bipolarity carried out by the Municipal Education System as a explicit control and regulation toll, related to the classification and learning in a interaction process that operates both in the pressure and the reflection, as a culture practice established between excellence of logic and learning. The evaluation history has been construct on the evaluation actions dialectics, joint simultaneously between the Institutional Evaluation Performance and the learning evaluation. The senses, meanings and actions bipolarity is a interaction process product sustained between the institutional evaluation, under the scholar ranking application, and the learning evaluation. In this relativity, the teacher evaluation practice is found, ruled by interesting, thoughts and actions on the school evaluation, allowing a higher security and support to the learning results. Grounded in the researched reality, its possible to say that the teacher s evaluation practice is diversified, with different characteristics, when it is done in the learning search and in the learning intention. In the first case, reflects, rearranges and constructs new actions that lead the student to produce learning. In the second, shows the will, the wish of learning, but is a weak action, producing a not really significant learning and development; as a result, remains the mark approach as a determinant in the student future. The work s hope is to contribute not just to rethink these two evaluations dimensions the institutional and the learning ones but also to organize the school and to improve the pedagogic process

Algoritmos genéticos: uso de lógica nebulosa e análise de convergência por cadeia de Markov

In this work, the Markov chain will be the tool used in the modeling and analysis of convergence of the genetic algorithm, both the standard version as for the other versions that allows the genetic algorithm. In addition, we intend to compare the performance of the standard version with the fuzzy version, believing that this version gives the genetic algorithm a great ability to find a global optimum, own the global optimization algorithms. The choice of this algorithm is due to the fact that it has become, over the past thirty yares, one of the more importan tool used to find a solution of de optimization problem. This choice is due to its effectiveness in finding a good quality solution to the problem, considering that the knowledge of a good quality solution becomes acceptable given that there may not be another algorithm able to get the optimal solution for many of these problems. However, this algorithm can be set, taking into account, that it is not only dependent on how the problem is represented as but also some of the operators are defined, to the standard version of this, when the parameters are kept fixed, to their versions with variables parameters. Therefore to achieve good performance with the aforementioned algorithm is necessary that it has an adequate criterion in the choice of its parameters, especially the rate of mutation and crossover rate or even the size of the population. It is important to remember that those implementations in which parameters are kept fixed throughout the execution, the modeling algorithm by Markov chain results in a homogeneous chain and when it allows the variation of parameters during the execution, the Markov chain that models becomes be non - homogeneous. Therefore, in an attempt to improve the algorithm performance, few studies have tried to make the setting of the parameters through strategies that capture the intrinsic characteristics of the problem. These characteristics are extracted from the present state of execution, in order to identify and preserve a pattern related to a solution of good quality and at the same time that standard discarding of low quality. Strategies for feature extraction can either use precise techniques as fuzzy techniques, in the latter case being made through a fuzzy controller. A Markov chain is used for modeling and convergence analysis of the algorithm, both in its standard version as for the other. In order to evaluate the performance of a non-homogeneous algorithm tests will be applied to compare the standard fuzzy algorithm with the genetic algorithm, and the rate of change adjusted by a fuzzy controller. To do so, pick up optimization problems whose number of solutions varies exponentially with the number of variables

Automação da detecção de fraudes em sistemas de medição de energia elétrica utilizando lógica fuzzy em ambiente SCADA

This works presents a proposal to make automatic the identification of energy thefts in the meter systems through Fuzzy Logic and supervisory like SCADA. The solution we find by to collect datas from meters at customers units: voltage, current, power demand, angles conditions of phasors diagrams of voltages and currents, and taking these datas by fuzzy logic with expert knowledge into a fuzzy system. The parameters collected are computed by fuzzy logic, in engineering alghorithm, and the output shows to user if the customer researched may be consuming electrical energy without to pay for it, and these feedbacks have its own membership grades. The value of this solution is a need for reduce the losses that already sets more than twenty per cent. In such a way that it is an expert system that looks for decision make with assertivity, and it looks forward to find which problems there are on site and then it wont happen problems of relationship among the utility and the customer unit. The database of an electrical company was utilized and the datas from it were worked by the fuzzy proposal and algorithm developed and the result was confirmed

Lógica Fuzzy para Controle de pH em um Processo Petrolífero

This work proposes the design, the performance evaluation and a methodology for tuning the initial MFs parameters of output of a function based Takagi-Sugeno-Kang Fuzzy-PI controller to neutralize the pH in a stirred-tank reactor. The controller is designed to perform pH neutralization of industrial plants, mainly in units found in oil refineries where it is strongly required to mitigate uncertainties and nonlinearities. In addition, it adjusts the changes in pH regulating process, avoiding or reducing the need for retuning to maintain the desired performance. Based on the Hammerstein model, the system emulates a real plant that fits the changes in pH neutralization process of avoiding or reducing the need to retune. The controller performance is evaluated by overshoots, stabilization times, indices Integral of the Absolute Error (IAE) and Integral of the Absolute Value of the Error-weighted Time (ITAE), and using a metric developed by that takes into account both the error information and the control signal. The Fuzzy-PI controller is compared with PI and gain schedule PI controllers previously used in the testing plant, whose results can be found in the literature.

Sistema automatizado para o aproveitamento de água cinza e azul, com controle de PH utilizando lógica fuzzy

Every day, water scarcity becomes a more serious problem and, directly affects global society. Studies are directed in order to raise awareness of the rational use of this natural asset that is essential to our survival. Only 0.007% of the water available in the world have easy access and can be consumed by humans, it can be found in rivers, lakes, etc... To better take advantage of the water used in homes and small businesses, reuse projects are often implemented, resulting in savings for customers of water utilities. The reuse projects involve several areas of engineering, like Environmental, Chemical, Electrical and Computer Engineering. The last two are responsible for the control of the process, which aims to make gray water (soapy water), and clear blue water (rain water), ideal for consumption, or for use in watering gardens, flushing, among others applications. Water has several features that should be taken into consideration when it comes to working its reuse. Some of the features are, turbidity, temperature, electrical conductivity and, pH. In this document there is a proposal to control the pH (potential Hydrogen) through a microcontroller, using the fuzzy logic as strategy of control. The controller was developed in the fuzzy toolbox of Matlab®

Sistema para detecção e diagnóstico de falhas em motores elétricos de indução utilizando lógica fuzzy

Induction motors are one of the most important equipment of modern industry. However, in many situations, are subject to inadequate conditions as high temperatures and pressures, load variations and constant vibrations, for example. Such conditions, leaving them more susceptible to failures, either external or internal in nature, unwanted in the industrial process. In this context, predictive maintenance plays an important role, where the detection and diagnosis of faults in a timely manner enables the increase of time of the engine and the possibiity of reducing costs, caused mainly by stopping the production and corrective maintenance the motor itself. In this juncture, this work proposes the design of a system that is able to detect and diagnose faults in induction motors, from the collection of electrical line voltage and current, and also the measurement of engine speed. This information will use as input to a fuzzy inference system based on rules that find and classify a failure from the variation of thess quantities

Controle de Temperatura do Sistema de Refrigeração a água de uma tocha plasmática Indutiva Utilizando Lógica fuzzy

Este projeto propõe desenvolver e implementar um controlador para o sistema de refrigeração da tocha indutiva a plasma térmico. Este processo é feito a partir da medição da temperatura através de um sensor do sistema de refrigeração. O sinal produzido será enviado para uma entrada analógica do microcontrolador da família PIC, que utilizando os conceitos de lógica fuzzy, controla a velocidade de um motor bomba. Este é responsável por diminuir ou aumentar o fluxo circulante de água que passa pela bobina, pelo corpo da tocha e pelo flange de fixação, deixando-os na temperatura desejada. A velocidade desta bomba será controlada por um inversor de frequência. O microcontrolador, também, acionará um ventilador caso exceda a temperatura de referência. A proposta inicial foi o desenvolvimento do controle da temperatura da bobina de uma tocha indutiva a plasma, mas com algumas adequações, foi possível também aplicar no corpo da tocha. Essa tocha será utilizada em uma planta de tratamento de resíduos industriais e efluentes petroquímicos. O controle proposto visa garantir as condições físicas necessárias para tocha de plasma, mantendo a temperatura da água em um determinado nível que permita o resfriamento sem comprometer, no entanto, o rendimento do sistema. No projeto será utilizada uma tocha de plasma com acoplamento indutivo (ICPT), por ter a vantagem de não possuir eletrodos metálicos internos sendo erodidos pelo jato de plasma, evitando uma possível contaminação, e também devido à possibilidade do reaproveitamento energético através da cogeração de energia. O desenvolvimento da tecnologia a plasma na indústria de tratamento de resíduos vem obtendo bons resultados. Aplicações com essa tecnologia têm se tornado cada vez mais importantes por reduzir, em muitos casos, a produção de resíduos e o consumo de energia em vários processos industriais

Utilização da lógica difusa no controle inteligente de sistemas eletro-hidráulicos

Electro-hydraulic servo-systems are widely employed in industrial applications such as robotic manipulators, active suspensions, precision machine tools and aerospace systems. They provide many advantages over electric motors, including high force to weight ratio, fast response time and compact size. However, precise control of electro-hydraulic systems, due to their inherent nonlinear characteristics, cannot be easily obtained with conventional linear controllers. Most flow control valves can also exhibit some hard nonlinearities such as deadzone due to valve spool overlap on the passage´s orifice of the fluid. This work describes the development of a nonlinear controller based on the feedback linearization method and including a fuzzy compensation scheme for an electro-hydraulic actuated system with unknown dead-band. Numerical results are presented in order to demonstrate the control system performance

Lógica condicional

The main goal of this work is to clarify the central concepts involved in the study of formalization of conditional sentences. More specifically, it has been done a comparative analysis of the two greater and more traditional proposals of conditional formalization (Lewis 1973c e Adams 1975). These proposals were responsible for the creation of a way of analysis that still present in the current debate about this subject. This work pursues to explain the principal assumptions held within these proposals. According to certain disambiguation techniques from Bennett (2003) and Lycan (2005), this work tries to explicit how these assumptions connect to the aims sought by the initial approaches. The following results show that there is a not declared presumption, the definition of the object of study of these theories, i.e., the definition of conditional sentence. This work argues that despite of not explicitly declared the definition of the study object has a central role in the intelligibility of the debate itself

Sistemas de lógica modal em dedução natural

Formalization of logical systems in natural deduction brings many metatheoretical advantages, which Normalization proof is always highlighted. Modal logic systems, until very recently, were not routinely formalized in natural deduction, though some formulations and Normalization proofs are known. This work is a presentation of some important known systems of modal logic in natural deduction, and some Normalization procedures for them, but it is also and mainly a presentation of a hierarchy of modal logic systems in natural deduction, from K until S5, together with an outline of a Normalization proof for the system K, which is a model for Normalization in other systems

Lógica por trás dos contratos sociais

Natural selection shapes body and behavior of each species. For primates, the social environment constituted one of the greatest selective pressure for the development of their cognition. When we consider gender differences, we see that sexual selection also operates through different selective pressures for men and women not only in physical terms but in terms of cognitive skills. Among these, the primary cognitive abilities - that emerge naturally - and secondary - that rely on an artificial environment for learning - develop differently for each sex, making them suitable for specific tasks in different capacities. Previous studies utilized the Wason Selection Test a conditional logic tool - to measure, among several other things, the ability to recognize violation of rules in abstract contexts and social contexts. Subjects generally had better performance in the latter, however, in these studies possible differences motivated by learning in formal logic or genre were not considered. Our study investigated these two variables, as well as the time spent to solve each task. Furthermore, we used an index to take into account the rights and wrongs of the participants in tasks. We realized that although learning in formal logic does not bring significant differences in solving tests, the gender differences are strongly observed when we consider the social contexts and abstract. Women perform better in social tasks. This can be explained due to different sexual selective pressures for this gender in terms of one-on-one relationships within the group. Men are better at tasks of abstract context and this is probably due to the same reason. Their capabilities for territory defense, habitat navigation and forming coalitions depends on primary cognitive abilities that support secondary cognitive skills of abstraction. Thus, gender differences are a factor to be taken into account in controlling future experiments with the same tool