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In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p -adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert ’s style, sequent, and hypersequent. Recall that hypersequents are a natural generalization of Gentzen ’s style sequents that was introduced independently by Avron and Pottinger . In particular, we examine Hilbert ’s style, sequent, and hypersequent calculi for infinite-valued logics based on the three fundamental continuous t-norms: Lukasiewicz ’s, Godel ’s, and Product logics....

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1.1 Neutrality concept in logic Every point of view A tends to be neutralized, diminished, balanced by Non-A. At the same time, in between A and Non-A there are infinitely many points of view Neut-A. Let’s note by A an idea, or proposition, theory, event, concept, entity, by Non-A what is not A, and by Anti-A the opposite of A. Neut-A means what is neither A nor Anti-A, i.e. neutrality is also in between the two extremes. ...

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1 Introduction. . . . . . . . . . . . . . . 9 1.1 Neutrality concept in logic . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Neutrality and non-Archimedean logical multiple-validity . . . . 10 1.3 Neutrality and neutrosophic logic . . . . . . . . . . . . . . . . . . 13 2 First-order logical language. . . . . . . . . . . . . . . 17 2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Hilbert’s type calculus for classical logic . . . . . . . . . . . . . . 20 2.3 Sequent calculus for classical logic . . . . . . . . . . . . . . . . . 22 3 n -valued Lukasiewicz’s logics. . . . . . . . . . . . . . . 27 3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Originality of (p + 1)-valued Lukasiewicz’s logics . . . . . . . . . 30 3.3 n-valued Lukasiewicz’s calculi of Hilbert’s type . . . . . . . . . . 32 3.4 Sequent calculi for n-valued Lukasiewicz’s logics . . . . . . . . . . 33 3.5 Hypersequent calculus for 3-valued Lukasiewicz’s propositional logic . . . . . . . . . . . .37 4 Infinite valued Lukasiewicz’s logics. . . . . . . . . . . . . . . 39 4.1 Prelimi...

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A book on the contrasts between the eastern Asian culture versus the western culture on topics such as education, medicine, science, and politics.

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Is oriental culture a kind of science? There lies a crucial difference in that Western science seeks the exterior solutions outside the heart. However, our ancient sages illustrated that humans are an integral part of the universe, and all the phenomena never skip out of the heart. And very fortunately, many wise men did succeed in cultivating their hearts to testify to the profound truth. So our Eastern classics focus on our inner cultivation. However people, including the overwhelming majority of the Chinese, would regard such education as being an extra (to life or science). Please contact the corresponding Taiwan or Singapore websites, where there are plenty of English versions of texts and videos of Buddhism, to request the standard translation. “What is Dao (Tao)? It is the natural principle all over the universe, the natural order, the essentiality of nature. The great universe has its order and rule, where the education of ancient sages roots. Education stems from here, and a human being has to obey the natural principle –Dao. In our Chinese notion of the integral of humans and nature; heaven, earth and human are...

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On the Cultural Contrast: East-West, preface by F. Liu .……………………………….4 Abstract by the Translator to the Chinese Translation of Neutrosophics………………12 Preface by the Translator to the Chinese Translation of Neutrosophics………………13 Biography of the Translator…………………………………………………………….18 Publication Review by F. Liu…………………………………………………………22 Annotation in the Chinese Translation of Neutrosophics………………………………27 Neutrosophic Dialogues………………………………………………………………51 Absolute Truth……………………………………………………………………………68 Science, Destiny, and Buddhism……………………………………………………….…79 Call for Papers…………………………………………………………………………….94 Neutrosophy and Dialectic, postface by Anthony Mansueto.…………………………….95...

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The authors in this book have analyzed the socio-economic and psychological problems faced by People with Disabilities (PWDs) and their families. The study was made by collecting data using both fuzzy linguistic questionnaire by interviews in case they are not literates from 2,15,811 lakhs people. This data was collected using the five Non Government Organizations (NGOs) from northern Tamil Nadu....

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The main objective of this was to understand the basic psychological and social problems faced by the PWDs and their caretakers. To interpret the collected data, tabulations and analysis were made. Efforts were made to highlight the inferences in each table and in few places comments were made in order to use it for fuzzy analysis. Following is the list of organizations and the total population from 5 blocks is listed below....

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Preface 6 Chapter One INTRODUCTION TO BASIC CONCEPTS 11 Chapter Two ANALYSIS OF THE COLLECTED DATA OF THE PWDS FROM MELMALAYANUR AND KURINJI PADI BLOCKS IN TAMIL NADU 13 Chapter Three THE NEW FUZZY COGNITIVE RELATIONAL MAPS (FCRMS) BIMODEL 29 Chapter Four ANALYSIS OF THE SOCIO ECONOMIC PROBLEMS FACED BY THE PWDS USING (SFCMS) 47 4.1 Application of FCMs Models to Social and Psychological Problems 48 4.2 Expert Opinion of PWDs using Special FCMs to Analyse the Problem of PWDs 50 4.3 The Expert Opinion of the caretakers of the PWDs using SFCM 59 4.4 The Expert Opinion of the NGOs working with the PWDs using Special FCM Model 62 Chapter Five THE STUDY OF INTERRELATED PROBLEMS FACED BY THE PWDS AND THE CARE TAKERS 73 5.1 Introduction 73 5.2 Experts Opinion from a Public Person Living in Melmalayanur Block 77 5.3 Expert Opinion of PWDs using FRMs 84 5.4 Expert Opinion of Caretakers of the PWDs using FRM 87 5.5 Expert Opinion of the NGOs working with the PWDs using the FRM model 93 Chapter Six ANALYSIS OF PROBLEMS OF RURAL PWDs USING THE NEW FCRM BIMODEL 99 6.1 Expert Opinion of the Caretaker and a PWD using the ...

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Applications demonstrate the power of the DSmT framework. In this third Volume, DSmT is applied to the entire spectrum of the Information Fusion that would interest any reader in data, sensor, information, and mathematical fusion topics. Highlighted in Figure 1 are the contemporary issues that include the links between (1) data conditioning and information management, (2) combined situation and impact assessment, and (2) knowledge representation between machine processing and user coordination. Various applications leverage DSmT “Advances” listed above along with DSmH (hybrid), DSmP (Probabilistic), and DSmT theoretical insights. The third volume attacks these application issues of coordination between the “levels” of information fusion....

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...Part I Advances on DSmT 1 Chapter 1 An introduction to DSmT 3 by J. Dezert and F. Smarandache 1.1 Introduction . . . . . . . . . . 4 1.2 Foundations of DSmT . . . . . . . . . 4 1.2.1 The power set, hyper-power set and super-power set . . 6 1.2.2 Notion of free and hybrid DSm models . . . . 18 1.2.3 Ge...

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...This second book devoted on advances and applications of Dezert-Smarandache Theory (DSmT) for information fusion collects recent papers from different researchers working in engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical investigation...

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...Preamble iii Prefaces v Part I Advances on DSmT 1 Chapter 1 Proportional Conflict Redistribution Rules for Information Fusion 3 by Florentin Smarandache and Jean Dezert 1.1 Introduction . . . . . . . . . . . 3 1.2 The principal rules of combination . . . . . . . 6 1.2.1 Notion of total and partial conflicting masses . . . . . 6 1.2.2 The conjunctive ...

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...n the information provided by the sources is both uncertain and (highly) conflicting. This approach, known in literature as DSmT (standing for Dezert-Smarandache Theory), proposes new useful rules of combinations. We gathered in this volume a presentation of DSmT from the beginning to the latest development. Part 1 of this book presents the current state-of-the-art on theo...

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...57 8.2.1 Preliminary: about probability . . . 157 8.2.2 Dempster Shafer Theory . . . . 161 8.2.3 Transferable Belief Model . . . . 162 8.3 Dezert Smarandache Theory (DSmT) . . . 163 8.3.1 Dezert Smarandache model . . . . 164 8.3.2 Fusion rule . . . . . 166 8.4 Probability over logical propositions . . . . 167 8.4.1 Definition . . . . . 167 8.4.2 Property . . . . ....

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The authors use linguistic paradoxes, play against the grain on linguistic clichés, and employ mathematical combinations of words involving contradictions, antitheses, oxymoron, which fully characterize the paradoxism movement in literature and science....

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A descris ceva de nedescris. ● Unul venea după bani, iar celălalt după amiază. ● Memoria, fiind de genul feminin, mă cam înşeală. ● A avut o tentativă de omor prin imprudenţă. ● El a rămas repetent, iar ea a rămas gravidă. ● A legat un cal putere de un arbore cotit, într-un câmp electromagnetic. ● Unul avea ochi albaştri, iar celălalt avea darul beţiei. ● L-a scos din minţi şi l-a băgat în spital. ● Nevasta generalului în retragere era mereu în atac. ● Este fondatorul unui partid extremist de centru. ● Elevii de la şcoala de marină învăţau lecţiile ca pe apă. ● I-a venit pe chelie să-şi lase plete. ● Era în stare de staţionare interzisă. ● Îi merge vorba că ar fi mut. ● A avut o cădere înălţătoare: din lac în puţ. ● Culmea fericirii: să pleci bou şi să te întorci taur. ● De ce le zice pui de găină, dacă mama lor este o cloşcă? ● A împărţit un măr în trei jumătăţi inegale, în mod echitabil. He described the indescribable. ● One coming after money, and the other in the afternoon. ● Memory, being feminine, I kind of cheating. ● He had attempted manslaughter. ● He retained student, and she got pregnant. ● A tied...