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

A integração do tutorial interativo TryLogic via IMS Learning Tools Interoperability: construindo uma infraestrutura para o ensino de Lógica através de estratégias de demonstração e refutação

Logic courses represent a pedagogical challenge and the recorded number of cases of failures and of discontinuity in them is often high. Amont other difficulties, students face a cognitive overload to understand logical concepts in a relevant way. On that track, computational tools for learning are resources that help both in alleviating the cognitive overload scenarios and in allowing for the practical experimenting with theoretical concepts. The present study proposes an interactive tutorial, namely the TryLogic, aimed at teaching to solve logical conjectures either by proofs or refutations. The tool was developed from the architecture of the tool TryOcaml, through support of the communication of the web interface ProofWeb in accessing the proof assistant Coq. The goals of TryLogic are: (1) presenting a set of lessons for applying heuristic strategies in solving problems set in Propositional Logic; (2) stepwise organizing the exposition of concepts related to Natural Deduction and to Propositional Semantics in sequential steps; (3) providing interactive tasks to the students. The present study also aims at: presenting our implementation of a formal system for refutation; describing the integration of our infrastructure with the Virtual Learning Environment Moodle through the IMS Learning Tools Interoperability specification; presenting the Conjecture Generator that works for the tasks involving proving and refuting; and, finally to evaluate the learning experience of Logic students through the application of the conjecture solving task associated to the use of the TryLogic

Industrialização e emprego formal: uma análise para os municípios da região metropolitana do Cariri nos anos de 1990 e 2000

The Northeast has a record of fighting to reduce disparities. In late 1950, the state intervened through SUDENE, organizing and planning the promotion of development through industrialization. This study aims to identify the characteristics of the industrialization of the Northeast and evolution of formal employment in the metropolitan area of Cariri, located in the southern state of Ceará, in the case of the municipalities of Crato, Juazeiro do Norte and Barbalha (CRAJUBAR) in decades of 1990 and 2000. The assumption permeates the SUDENE with public policies to encourage the industry, causing profound changes in the cities studied. The results indicate that the Cariri since the 1960 has been benefiting the programs implemented by SUDENE. With the implementation of these programs, with in a set of circumstances based on local vocations and state policies, there was a spatial distribution industry, triggering a growth and development on the provision of formal jobs in the industrial sector

Uma educação tecida no corpo

In theory say the education as a knot of meanings made in the body. We take as a reference for demonstration of this argument the shows Folguedos, Guarnicê and Flor do Lírio and built within such spectacles cultural, symbolic and aesthetic meanings, which reveal the education woven in the body. Education that can happen not only in the formal space like the classroom or the university, but also in the area of art and the inclusion of individuals in the world of culture. So during the construction of the thesis we reflect on the following issues: what is the construction of culture and art that have in the Parafolclórico group? What way theses shows in their buildings bring significant elements that might compose an educational activity. How objectives sought asking the dichotomies present in the concepts of art and culture; critically systematize a work of artistic, cultural and educational production in the group, in addition to expanding the understanding of education, considering the body experiences. The phenomenological attitude of Merleau-Ponty, is a reference methodology of this study, which places the reference knowledge as a result of our experience in the world, our world lived. Thus, this study considers the experience of the researcher in the three shows in tariff, represented by scenes described, as a dancer and spectator. Therefore we understand that Folguedos, Guarnicê and Flor do Lírio in their artistic, aesthetic and cultural languages, allow many meanings that occur in the body, which invites the perception and extend the experience of the subject, demonstrating an education that allows sight and knowledge, seeking new sensations and experiences, we show our intimacy with the world, with the objects and with the other. The art is understood as virtuality, as a human creation that carries the reality and that allows many readings and experiences, each perception can recognize and know new horizons, having as base and material the culture. This entails the heterogeneous, is not closed but that individuals can interpret it entered and recognize the symbols they created the same way, confirming a unit. The art and culture show us significant evidences of an education woven in the body

Uma proposta de regulador nebuloso para geradores eólicos de indução

This work presents a proposal for a voltage and frequency control system for a wind power induction generator. It has been developed na experimental structure composes basically by a three phase induction machine, a three phase capacitor and a reactive static Power compensator controlled by histeresys. lt has been developed control algorithms using conventional methods (Pl control) and linguistic methods (using concepts of logic and fuzzy control), to compare their performances in the variable speed generator system. The control loop was projected using the ADJDA PCL 818 model board into a Pentium 200 MHz compu ter. The induction generator mathematical model was studied throught Park transformation. It has been realized simulations in the Pspice@ software, to verify the system characteristics in transient and steady-state situations. The real time control program was developed in C language, possibilish verify the algorithm performance in the 2,2kW didatic experimental system

Arquitetura de controladores fuzzy em redes foundation fieldbus

Foundation Fieldbus Industrial networks are the high standard technology which allows users to create complex control logic and totally decentralized. Although being so advanced, they still have some limitations imposed by their own technology. Attempting to solve one of these limitations, this paper describes how to design a Fuzzy controller in a Foundation Fieldbus network using their basic elements of programming, the functional blocks, so that the network remains fully independent of other devices other than the same instruments that constitute it. Moreover, in this work was developed a tool that aids this process of building the Fuzzy controller, setting the internal parameters of functional blocks and informing how many and which blocks should be used for a given structure. The biggest challenge in creating this controller is exactly the choice of blocks and how to arrange them in order to effectuate the same functions of a Fuzzy controller implemented in other kind of environment. The methodology adopted was to divide each one of the phases of a traditional Fuzzy controller and then create simple structures with the functional blocks to implement them. At the end of the work, the developed controller is compared with a Fuzzy controller implemented in a mathematical program that it has a proper tool for the development and implementation of Fuzzy controllers, obtaining comparatives graphics of performance between both

Lógica BDI fuzzy

Intendding to understand how the human mind operates, some philosophers and psycologists began to study about rationality. Theories were built from those studies and nowadays that interest have been extended to many other areas such as computing engineering and computing science, but with a minimal distinction at its goal: to understand the mind operational proccess and apply it on agents modelling to become possible the implementation (of softwares or hardwares) with the agent-oriented paradigm where agents are able to deliberate their own plans of actions. In computing science, the sub-area of multiagents systems has progressed using several works concerning artificial intelligence, computational logic, distributed systems, games theory and even philosophy and psycology. This present work hopes to show how it can be get a logical formalisation extention of a rational agents architecture model called BDI (based in a philosophic Bratman s Theory) in which agents are capable to deliberate actions from its beliefs, desires and intentions. The formalisation of this model is called BDI logic and it is a modal logic (in general it is a branching time logic) with three access relations: B, D and I. And here, it will show two possible extentions that tranform BDI logic in a modal-fuzzy logic where the formulae and the access relations can be evaluated by values from the interval [0,1]

Geração automática de testes a partir de descrições de linguagens

Some programs may have their entry data specified by formalized context-free grammars. This formalization facilitates the use of tools in the systematization and the rise of the quality of their test process. This category of programs, compilers have been the first to use this kind of tool for the automation of their tests. In this work we present an approach for definition of tests from the formal description of the entries of the program. The generation of the sentences is performed by taking into account syntactic aspects defined by the specification of the entries, the grammar. For optimization, their coverage criteria are used to limit the quantity of tests without diminishing their quality. Our approach uses these criteria to drive generation to produce sentences that satisfy a specific coverage criterion. The approach presented is based on the use of Lua language, relying heavily on its resources of coroutines and dynamic construction of functions. With these resources, we propose a simple and compact implementation that can be optimized and controlled in different ways, in order to seek satisfaction the different implemented coverage criteria. To make the use of our tool simpler, the EBNF notation for the specification of the entries was adopted. Its parser was specified in the tool Meta-Environment for rapid prototyping

Estendendo CRefine para o suporte de táticas de refinamento

The use of increasingly complex software applications is demanding greater investment in the development of such systems to ensure applications with better quality. Therefore, new techniques are being used in Software Engineering, thus making the development process more effective. Among these new approaches, we highlight Formal Methods, which use formal languages that are strongly based on mathematics and have a well-defined semantics and syntax. One of these languages is Circus, which can be used to model concurrent systems. It was developed from the union of concepts from two other specification languages: Z, which specifies systems with complex data, and CSP, which is normally used to model concurrent systems. Circus has an associated refinement calculus, which can be used to develop software in a precise and stepwise fashion. Each step is justified by the application of a refinement law (possibly with the discharge of proof obligations). Sometimes, the same laws can be applied in the same manner in different developments or even in different parts of a single development. A strategy to optimize this calculus is to formalise these application as a refinement tactic, which can then be used as a single transformation rule. CRefine was developed to support the Circus refinement calculus. However, before the work presented here, it did not provide support for refinement tactics. The aim of this work is to provide tool support for refinement tactics. For that, we develop a new module in CRefine, which automates the process of defining and applying refinement tactics that are formalised in the tactic language ArcAngelC. Finally, we validate the extension by applying the new module in a case study, which used the refinement tactics in a refinement strategy for verification of SPARK Ada implementations of control systems. In this work, we apply our module in the first two phases of this strategy