Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2017-02-02T14:41:50Z No. of bitstreams: 1 JeffersonAlexandreDoNascimento_DISSERT.pdf: 6450548 bytes, checksum: 492fdc86c5c402671b6257d90803e044 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2017-02-09T17:30:36Z (GMT) No. of bitstreams: 1 JeffersonAlexandreDoNascimento_DISSERT.pdf: 6450548 bytes, checksum: 492fdc86c5c402671b6257d90803e044 (MD5) / Made available in DSpace on 2017-02-09T17:30:36Z (GMT). No. of bitstreams: 1 JeffersonAlexandreDoNascimento_DISSERT.pdf: 6450548 bytes, checksum: 492fdc86c5c402671b6257d90803e044 (MD5) Previous issue date: 2016-08-09 / A presente disserta??o tem por objetivo principal, apresentar uma proposta de ensino da l?gica matem?tica no ?mbito do Ensino M?dio, elencando fatores que baseados nos principais documentos oficiais que regem a educa??o no Brasil, mostram a import?ncia da inser??o da l?gica na grade curricular do Ensino M?dio. O trabalho est? dividido em 4 partes, nas quais est?o apresentadas a hist?ria da l?gica proposicional, a teoria, aplica??es da l?gica nas demonstra??es matem?ticas e atividades propostas ? serem aplicadas em sala de aula. / This work has as main objective to present a proposal for logic teaching mathematics in the high school, listing factors based on key documents official governing education in Brazil, show the importance of logic integration in curriculumof high school . The work is divided into 4 parts, which are presented in the history of propositional logic, theory, logic applications in mathematical demonstrations and activities proposed to They are applied in the classroom.

Submitted by Celso Magalhaes (celsomagalhaes@ufrrj.br) on 2017-05-31T17:28:56Z No. of bitstreams: 1 2016 - Pablo Vieira Carvalho Silva.pdf: 1591495 bytes, checksum: 23e5c1de4092f3df312f440079012ae0 (MD5) / Made available in DSpace on 2017-05-31T17:28:56Z (GMT). No. of bitstreams: 1 2016 - Pablo Vieira Carvalho Silva.pdf: 1591495 bytes, checksum: 23e5c1de4092f3df312f440079012ae0 (MD5) Previous issue date: 2016-06-30 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - CAPES / The mathematical logic has been removed and forgotten from the curriculum minimum of basic education for some time, despite the clear benefit that it can add to the student?s cognitive not only in mathematics study but also in his day by day decision-making. This study aims to rescue the discussion of its importance to the study in the basic levels, not doing it by traditional ways, but through problem solving techniques also using the Polya phases. Joining to this work, there are activities that were applied to a first year group of high school at a public school in Rio de Janeiro. / A l?gica matem?tica h? algum tempo foi retirada e esquecida do curr?culo m?nimo do ensino b?sico da educa??o brasileira, mesmo diante dos claros benef?cios que a mesma pode acrescentar ao cognitivo do educando n?o s? no estudo da matem?tica como em tomadas de decis?es do seu dia a dia. Este trabalho tem por finalidade resgatar a discuss?o de sua import?ncia para o estudo nas s?ries b?sicas, n?o o fazendo por vias tradicionais, mas sim atrav?s de t?cnicas de resolu??o de problemas utilizando tamb?m para isso as fases de Polya. Junto deste trabalho, apresentamos atividades aplicadas ao primeiro ano do ensino m?dio de uma escola estadual do Rio de Janeiro

Submitted by Setor de Tratamento da Informa??o - BC/PUCRS (tede2@pucrs.br) on 2015-07-20T11:50:24Z No. of bitstreams: 1 472408 - Texto Completo.pdf: 512200 bytes, checksum: 5f63e80e4169224eed290a1843d451b0 (MD5) / Made available in DSpace on 2015-07-20T11:50:24Z (GMT). No. of bitstreams: 1 472408 - Texto Completo.pdf: 512200 bytes, checksum: 5f63e80e4169224eed290a1843d451b0 (MD5) Previous issue date: 2015-03-27 / This is a qualitative research, a study case. As a question of research it poses the following problem: How are the different conceptions of logic inserted in the teaching practice of a mathematics teachers? group in High School? Its main objective is to understand the insertion of the different logic conceptions in the teaching practice of a group of mathematics teachers in High School. In order to achieve this goal, the following specific objectives are considered: (1) Identify the different logic conceptions of a group of mathematics teachers in High School; (2) Understand how these teachers realize the presence of logic in their pedagogical practice; and (3) Identify the different logic conceptions present in pedagogical support materials used by these teachers. In the theoretical background the following themes are approached: Philosophy and Logic; The several conceptions of logic (Aristotle, Russell, Bacon, Decarte); The teaching and learning of logic. Six teachers who hold a degree in mathematics, teachers in the three grades of High School and the analysis of pedagogical support materials was made by the teachers. The data were submitted to the Discursive Textual Analysis. From the analysis the following categories emerged: Conceptions of the teachers about logic, The presence of the Logic in the teaching practice and The several conceptions of logic and the teaching material. In the first category showed that this group of teachers there is certain difficulty of defining what logic is. The group presented three definitions of logic which are: (1) all and any way of thinking; (2) all that can be explained through reason; and (3) sets of arguments that we use to validate or invalidate knowledge. Therefore, to the teachers, logic is the built of a solid argumentation, with coherent thinking, well structured, in order to be able to infer on premises, concepts, problem-situations and the reality, being able to modify them in a conscious way, based on reason, determining its validity and its falsity. In the second category, it became evident that all the teachers, somehow, approach logic in their teaching practices. They affirm that there is little time to teach logic as a topic or content of the subject. What refers to the approach of logic in its pedagogical practices, I evinced that this teachers? group use logic in their classes when they work with demonstrations, either in Mathematics or Physics subjects, when they work the connectives, with combinatorial and probability analysis, in problem solving, set theory, validation of arguments, true and false, and in all and any situation in which the teachers and students need to argument, solve a problem solving situation and interfere in the world and its reality. And in the third category, we evince that the logical conceptions that appear are the Cartesian ones, being this the most present, the conception of Wittgenstein, the Aristotelian conception and the Russell conception. Although these logical conceptions are present in their materials, none of the teachers identified them in an explicit way. This is, they affirm the presence of logic in their materials, but they do not identify which of the conceptions is present in their books, notebooks or booklets. / A pesquisa ? de natureza qualitativa, do tipo estudo de caso. Tem como quest?o de pesquisa o seguinte problema: De que modo as diferentes concep??es de L?gica est?o inseridas na pr?tica docente de um grupo de professores de Matem?tica de Ensino M?dio? Tem por objeto geral compreender a inser??o das diferentes concep??es de L?gica na pr?tica docente de um grupo de professores de Matem?tica de Ensino M?dio. Para atingir esse objetivo, s?o considerados os seguintes objetivos espec?ficos: (1) identificar as diferentes concep??es de l?gica de um grupo de professores de matem?tica do Ensino M?dio; (2) compreender como esses professores percebem a presen?a da L?gica na sua pr?tica pedag?gica; e (3) Identificar as diferentes concep??es de L?gica presentes em materiais de apoio pedag?gico utilizado por esses professores. Na fundamenta??o te?rica s?o abordados os seguintes temas: Filosofia e L?gica; As diversas concep??es de L?gica (Arist?teles Russell, Bacon, Descartes e Wittgenstein); A import?ncia da L?gica nos processos de ensino e de aprendizagem de Matem?tica. Foram entrevistados seis professores licenciados em Matem?tica, docentes nas tr?s s?ries do Ensino M?dio e realizada a an?lise de materiais de apoio pedag?gico utilizados pelos professores. Os dados foram submetidos ? An?lise Textual Discursiva. Da an?lise emergiram as seguintes categorias: Concep??es dos professores sobre L?gica, A presen?a da L?gica na pr?tica docente e As diversas concep??es de L?gica presentes no material did?tico. Na primeira categoria evidenciou-se que neste grupo de professores h? uma certa dificuldade em definir o que ? l?gica. O grupo apresentou tr?s defini??es de l?gica que s?o: (1) toda e qualquer forma de pensar; (2) tudo que pode ser explicado por meio da raz?o; e (3) conjuntos de argumentos que utilizamos para validar ou invalidar um conhecimento. Portanto, para os professores, L?gica ? a constru??o de uma argumenta??o s?lida, com pensamentos coerentes, bem estruturados, de modo que possamos inferir sobre premissas, conceitos, situa??es-problema e a realidade, podendo modific?-las de modo consciente, baseado na raz?o, determinando a sua validade e falsidade. Na segunda categoria, evidenciou-se que todos os professores, de alguma forma, abordam a L?gica em suas pr?ticas docentes. Afirmam que h? pouco tempo para se ensinar a L?gica como um t?pico ou conte?do da mat?ria. No que se refere ? abordagem da L?gica em suas pr?ticas pedag?gicas evidenciou-se que este grupo de professores utiliza a L?gica em suas aulas ao trabalhar com demonstra??es, seja nas disciplinas de Matem?tica ou F?sica, ao trabalhar com conectivos, com An?lise Combinat?ria e Probabilidade, na resolu??o de problemas, na teoria de conjuntos, na valida??o de argumentos, e em toda e qualquer situa??o em que professores e alunos necessitem argumentar, resolver uma situa??o-problema e interferir no mundo e em sua realidade. E na terceira categoria evidenciou-se que as concep??es de L?gica presentes no material did?tico s?o as concep??es Cartesiana, sendo esta a mais presente, a concep??o de Wittgenstein, a concep??o Aristot?lica e a concep??o de Russell. Embora essas concep??es l?gicas estejam presentes em seus materiais, nenhum dos professores as identificou de forma expl?cita. Isto ?, afirmam a presen?a da l?gica em seus materiais, mas n?o identificam qual das concep??es est? presente em seus livros, cadernos ou apostilas.

Made available in DSpace on 2014-12-17T14:35:50Z (GMT). No. of bitstreams: 1 GiselleCS_tese.pdf: 1424263 bytes, checksum: 0a3b291c39e9d1dfd7f82f5c1ef897a3 (MD5) Previous issue date: 2008-06-13 / 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 / O presente estudo tem como objetivo uma elucida??o das origens da l?gica matem?tica. Esta tem seu in?cio atribu?do ao matem?tico ingl?s autodidata George Boole (1815-1864), especialmente porque seus livros The Mathematical Analysis of Logic (1847) e An Investigation of the Laws of Thought (1854) s?o reconhecidos como as obras inaugurais do referido ramo. Contudo, curiosamente, na mesma ?poca um outro matem?tico chamado Augutus de Morgan (1806-1871) tamb?m lan?ou um livro, intitulado Formal Logic (1847), em defesa da matematiza??o da l?gica. Mesmo assim, tempos depois neste mesmo s?culo, uma outra obra nomeada Elements of Logic (1875) surgiu evidenciando a l?gica aristot?lica a partir da figura de Richard Whately (1787-1863), considerado o maior l?gico aristot?lico da ?poca. Desta forma, nossa pesquisa, permeada pela hist?ria da matem?tica, prop?e estudar a l?gica produzida por estes personagens imersos na idade ?urea da matem?tica (s?culo XIX) a fim de compararmos os sistemas vigentes no referido per?odo e clarificarmos as origens da l?gica matem?tica. Para isso buscamos delinear o panorama hist?rico envolt?rio deste estudo. Descrevemos, brevemente, considera??es biogr?ficas destes tr?s representantes da l?gica do s?culo XIX aliadas ? exposi??o de seus pontos de vista quanto ? l?gica ? luz das obras citadas acima. Neste sentido, aspiramos ainda apresentar considera??es acerca do que existia de l?gica aristot?lica vigente no per?odo de Boole e De Morgan comparando-a com a nova l?gica emergente (a l?gica matem?tica). Al?m disso, diante da an?lise textual das obras citadas acima, buscamos ainda confrontar os sistemas de Boole e De Morgan a fim de chegarmos ao motivo pelo o qual o de Boole ter sido considerado melhor e mais eficiente. ? parte desta preponder?ncia, almejamos estudar as falhas constatadas no sistema l?gico de Boole frente ? produ??o de seus contempor?neos, verificando, por exemplo, se elas se repetiram ou n?o. Conclu?mos que as origens da l?gica matem?tica residem nas obras de l?gica de George Boole, visto que, nelas, h? a apresenta??o de uma nova l?gica, matematizada pelas leis do pensamento an?logas ?s da aritm?tica, enquanto De Morgan conseguiu em seu trabalho expandir a l?gica aristot?lica, mas ainda esteve preso a ela

Made available in DSpace on 2015-03-03T15:47:47Z (GMT). No. of bitstreams: 1 PatrickCAT_DISSERT.pdf: 4794202 bytes, checksum: 05088b21ff2be2b3c2ccec958e7e6b62 (MD5) Previous issue date: 2013-06-03 / 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 / A disciplina de L?gica representa um desa o tanto para docentes como para discentes, o que em muitos casos resulta em reprova??es e desist?ncias. Dentre as dificuldades enfrentadas pelos alunos est? a sobrecarga da capacidade cognitiva para compreender os conceitos l?gicos de forma relevante. Neste sentido, as ferramentas computacionais de aprendizagem s?o recursos que auxiliam a redu??o de cen?rios de sobrecarga cognitiva, como tamb?m permitem a experi?ncia pr?tica de conceitos te?ricos. O presente trabalho prop?e uma tutorial interativo chamado TryLogic, visando ao ensino da tarefa de Demonstra??o ou Refuta??o (DxR) de conjecturas l?gicas. Trata-se de uma ferramenta desenvolvida a partir da arquitetura do TryOcaml atrav?s do suporte de comunica??o da interface web ProofWeb para acessar o assistente de demonstra??o de teoremas Coq. Os objetivos do TryLogic s?o: (1) Apresentar um conjunto de li??es para aplicar estrat?gias heur?sticas de an?lise de problemas em L?gica Proposicional; (2) Organizar em passo-a-passo a exposi ??o dos conte?dos de Dedu??o Natural e Sem?ntica Proposicional de forma sequencial; e (3) Fornecer aos alunos tarefas interativas. O presente trabalho prop?e tamb?m apresentar a nossa implementa??o de um sistema formal de refuta??o; descrever a integra??o de nossa infraestrutura com o Ambiente Virtual de Aprendizagem Moodle atrav?s da especi ca??o IMS Learning Tools Interoperability ; apresentar o Gerador de Conjecturas de tarefas de Demonstra??o e Refuta??o e, por m, avaliar a experi?ncia da aprendizagem de alunos de L?gica atrav?s da aplica??o da tarefa de DxR em associa??o ? utiliza??o do TryLogic

Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2017-04-03T22:46:24Z No. of bitstreams: 1 LauraFernandesDellOrto_DISSERT.pdf: 866111 bytes, checksum: 0ef11e74d1508214463b993885352d6c (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2017-04-11T20:56:41Z (GMT) No. of bitstreams: 1 LauraFernandesDellOrto_DISSERT.pdf: 866111 bytes, checksum: 0ef11e74d1508214463b993885352d6c (MD5) / Made available in DSpace on 2017-04-11T20:56:41Z (GMT). No. of bitstreams: 1 LauraFernandesDellOrto_DISSERT.pdf: 866111 bytes, checksum: 0ef11e74d1508214463b993885352d6c (MD5) Previous issue date: 2017-02-15 / Em L?gica Cl?ssica, podemos utilizar as hip?teses um n?mero indeterminado de vezes. Por exemplo, a prova de um teorema pode fazer uso do mesmo lema v?rias vezes. Por?m, em sistemas f?sicos, qu?micos e computacionais a situa??o ? diferente: um recurso n?o pode ser reutilizado ap?s ser consumido em uma a??o. Em L?gica Linear, f?rmulas s?o vistas como recursos a serem utilizados durante a prova. ? essa no??o de recursos que faz a L?gica Linear ser interessante para a modelagem de sistemas. Para tanto, a L?gica Linear controla o uso da contra??o e do enfraquecimento atrav?s dos exponenciais ! e ?. Este trabalho tem como objetivo fazer um estudo sobre a L?gica Linear com Subexponenciais (SELL), que ? um refinamento da L?gica Linear. Em SELL, os exponenciais da L?gica Linear possuem ?ndices, isto ?, ! e ? ser?o substitu?dos por !i e ?i, onde ?i? ? um ?ndice. Um dos pontos fundamentais de Teoria da Prova ? a prova da Elimina??o do Corte, que neste trabalho ? demonstrada tanto para L?gica Linear como para SELL, onde apresentamos detalhes que normalmente s?o omitidos. A partir do teorema de Elimina??o do Corte, podemos concluir a consist?ncia do sistema (para as l?gicas que estamos utilizando) e outros resultados como a propriedade de subf?rmula. O trabalho inicia-se com um cap?tulo de Teoria da Prova, e em seguida se faz uma exposi??o sobre a L?gica Linear. Assim, com essas bases, apresenta-se a L?gica Linear com Subexponenciais. SELL tem sido utilizada, por exemplo, na especifica??o e verifica??o de diferentes sistemas tais como sistemas bioqu?micos, sistemas de intera??o multim?dia e, em geral, em sistemas concorrentes com modalidades temporais, espaciais e epist?micas. Com essa base te?rica bastante clara, apresenta-se a especifica??o de um sistema bioqu?mico utilizando SELL. Al?m disso, apresentamos v?rias inst?ncias de SELL que tem interpreta??es interessantes do ponto de vista computacional. / In Classical Logic, we can use a given hypothesis an indefinite number of times. For example, the proof of a theorem may use the same lemma several times. However, in physical, chemical and computational systems, the situation is different: a resource cannot be reused after being consumed in one action. In Linear Logic, formulas are seen as resources to be used during a proof. This feature makes Linear Logic an interesting formalism for the specification and verification of such systems. Linear Logic controls the rules of contraction and weakening through the exponentials ! and ?. This work aims to study Linear Logic with subexponentials (SELL), which is a refinement of Linear Logic. In SELL, the exponentials of Linear Logic are decorated with indexes, i.e., ! and ? are replaced with !i and ?i, where ?i? is an index. One of the main results in Proof Theory is the Cut-Elimination theorem. In this work we demonstrate that theorem for both Linear Logic and SELL, where we present details that are usually omitted in the literature. From the Cut-Elimination Theorem, we can show, as a corollary, the consistency of the system (for the logics considered here) and other results as the subformula property. This work begins with an introduction to Proof Theory and then, it presents Linear Logic. On these bases, we present Linear Logic with subexponentials. SELL has been used, for example, in the specification and verification of various systems such as biochemical systems, multimedia interaction systems and, in general, concurrent systems with temporal, spatial and epistemic modalities. Using the theory of SELL, we show the specification of a biochemical system. Moreover, we present several instances of SELL that have interesting interpretations from a computational point of view.