...N 1-879585-76-6 American Research Press Rehoboth 1999, 2000, 2003 FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEU... ...-76-6 American Research Press Rehoboth 1999, 2000, 2003 FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, ... ...script from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philo... ...m the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - re... ...ables, odds, paradoxes in creations. It was set up and led by the writer Florentin Smarandache since 1980's, who said: "The goal is to enlargement ... ...s, paradoxes in creations. It was set up and led by the writer Florentin Smarandache since 1980's, who said: "The goal is to enlargement of the art... ...s) have been published, plus 3 national and international anthologies." (Florentin Smarandache) 2.4. Features of Paradoxism (by Florentin Smaranda... ...een published, plus 3 national and international anthologies." (Florentin Smarandache) 2.4. Features of Paradoxism (by Florentin Smarandache) # Ba... ...American speech of Tomorrow?)... [From the book: NonPoems, by Florentin Smarandache, Xiquan Publishing House, Phoenix, Chicago, 1991, 1992, 1993; ...

It was known to me his setting up in 1980’s of a new literary and artistic avant-garde movement that he called “paradoxism”, because I received some books and papers dealing with it in order to review them for the German journal “Zentralblatt fár Mathematik”. It was an inspired connection he made between literature/arts and science, philosophy....

Paradoxism is an avant-garde movement in literature, art, philosophy, science, based on excessive used of antitheses, antinomies, contradictions, parables, odds, paradoxes in creations....

...allup 1-3 December 2001 (second printed edition) FLORENTIN SMARANDACHE editor PROCEEDINGS OF THE FIRST INTERNATIO... ... 1-3 December 2001 (second printed edition) FLORENTIN SMARANDACHE editor PROCEEDINGS OF THE FIRST INTERNATIONAL CONFE... ...co Contributed papers were sent, by November 30, 2001, to the organizer: Florentin Smarandache, University of New Mexico, 200 College Road, Ga... ...ntributed papers were sent, by November 30, 2001, to the organizer: Florentin Smarandache, University of New Mexico, 200 College Road, Gallup, NM 8... ...Neutrosophic Conference). E-mail: smarand@unm.edu, http://www.gallup.unm.edu/~smarandache/FirstNeutConf.htm. A selection of them is being published... ...trosophics see the below links: • 0. Introduction: http://www.gallup.unm.edu/~smarandache/Introduction.PDF • 1. Neutrosophy - a new branch of philo... ...PDF • 1. Neutrosophy - a new branch of philosophy: http://www.gallup.unm.edu/~smarandache/Neutrosophy.PDF • 2. Neutrosophic Logic - a unifying fiel... ...ophic Logic, Neutrosophic Set, and Neutrosophic Probability and Statistics) Florentin Smarandache Department of Mathematics University of New Me... ...nal Journal of Intelligent Systems, Vol. I, 155-179, 1986. [39] Smarandache, Florentin, Α Unifying Field in Logics: Neutrosophic Logic. / Neutrosop...

As an alternative to the existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined, unknown, incompleteness, inconsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecision of the human systems is due to the imperfection of knowledge that humain receives (observation) from the external world. Imperfection leads to a doubt about the value of a variable, a decision to be taken or a conclusion to be drawn for the actual system. The sources of uncertainty can be stochasticity (the case of intrinsic imperfection where a typical and single value does not exist), incomplete knowledge (ignorance of the totality, limited view on a system because of its complexity) or the acquisition errors (intrinsically imperfect observations, the quantitative errors in measures).”...

...ADVENTURE How to Break the Light Barrier by A.D. 2070 Homer B. Tilton Florentin Smarandache 2 To the memory of Benjamin E. Tilton (1876-... ... How to Break the Light Barrier by A.D. 2070 Homer B. Tilton Florentin Smarandache 2 To the memory of Benjamin E. Tilton (1876-1955), a c... ...ooks can be downloaded from the E-Library of Science: www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm Production Editor Gloria Valles ... ...tment of Mathematics and Engineering Pima Community College, EC, USA Florentin Smarandache Department of Mathematics and Sciences The Universi... ...athematics and Engineering Pima Community College, EC, USA Florentin Smarandache Department of Mathematics and Sciences The University of New ... ...d deals with the transfer of information over large distances. Dr. Florentin Smarandache Associate Professor The University of New Mexico ... ...th the transfer of information over large distances. Dr. Florentin Smarandache Associate Professor The University of New Mexico at Gallup ... ...hers have also concluded there is no light barrier but for other reasons. Smarandache: [3] "There is no speed barrier in the universe." His reasonin... ... is real. To one riding on the charge it has no magnetic field. [3] Florentin Smarandache, There is no Speed Barrier in the Universe, Bulletin ...

For most of the 20th century, both relativity and star travel fascinated this writer. The reasons Albert Einstein concluded there is an absolute barrier at the speed of light seemed at first clear, then later not so clear upon closer examination. "The speed of light relative to what?" I often asked anyone who would listen. The common response was, "Light needs no specification of that kind; its speed is the same no matter who measures it." "That's true." I would respond; "That's just the second postulate of special relativity which is not in doubt; but that postulate applies to light, and we're talking about rocketships here." However it seemed that no one understood what I was saying. By referring to the universal constant c= 299.792 458 megameters per second as "the speed of light," we paint ourselves into a logical corner in which light is automatically taken as the subject of discussion even when it is not. The careful reader will know not to immediately think "light" when he hears or reads "the speed of light." But it is better to have a neutral name for that universal constant. It has been called the Lorentz speed; Ignaz...

One's reach should exceed one's grasp. Thus we reach for Alpha Centauri with a round-trip manned and womanned mission as the proposed overarching goal under a clear plan of exploration - a grand experiment described in later chapters. Whether or not we succeed in grasping the goal under this or under any plan is not as important as it is to set a definite plan and work towards its goal. The plan outlined here is in two phases: Phase one has a high probability of success, given the required propulsion system; the chances of phase two working will be indicated by results obtained from phase one. A fundamental problem is the one of propulsion. It is important to the working of this plan, a highly optimistic one, that the engine be capable of a sustained acceleration of ¼ G in phase one and 1G in phase two. (1G = 9.80665 m/s2) Such an engine is within the reach of present ideas....

Prefaces. 6 -- Ch.1. Introduction . 11 -- Ch.2. The Human Barrier. 14 -- Ch.3. An Overview. 18 -- Ch.4. Acceleration Due to Light Pressure. 21 -- Ch.5. Light Sailing is Not All There Is. 27 -- Ch.6. Einstein's Light Barrier. 32 -- Ch.7. The Phase One Experiment: The First Starship. 37 -- Ch.8. The Phase Two Experiment: Alpha Centauri or Bust!. 45 -- Ch.9. Voyage to the Center of the Galaxy. 50 -- Ch.10. An Hypothesis: There is no Speed Barrier in the Universe. 52 --...

Research papers presented in this collection manifest only a few of many possible applications of neutrosophic logics to theoretical physics. Most of these applications target the theory of relativity and quantum physics, but other sections of physics are also possible to be considered....

We apply the S-denying procedure to signature conditions in a four-dimensional pseudo-Riemannian space — i. e. we change one (or even all) of the conditions to be partially true and partially false. We obtain five kinds of expanded space-time for General Relativity. Kind I permits the space-time to be in collapse. Kind II permits the space-time to change its own signature. Kind III has peculiarities, linked to the third signature condition. Kind IV permits regions where the metric fully degenerates: there may be non-quantum teleportation, and a home for virtual photons. Kind V is common for kinds I, II, III, and IV....

...ivity, Gravitation, and Cosmology................6 S-Denying of the Signature Conditions Expands General Relativity’s Space, by Dmitri Rabounski, Florentin Smarandache, Larissa Borissova, Progress in Physics, 13-19, Vol. 3, 2006.......7 Positive, Neutral, and Negative Mass-Charges in General Relativity, by Larissa Borissova and Florentin Smarandache, Progress in Phy...

The whole paradoxist distich should be as a geometric unitary parabola, hyperbola, ellipse at the borders between art, philosophy, rebus, and mathematics – which exist in complementariness. The School of Paradoxist Literature, which evolved around 1980s, continues through these bi-verses closed in a new lyric exact formula, but with an opening to essence. For this kind of procedural poems one can elaborate mathematical algorithms and implement them in a computer: but, it is preferable a machine with … soul!...

I M M O D E S T With the shame Shamelessness U N D E C I D E D Fighting Himself J A Z Z ( I ) Melodious Anarchy J A Z Z ( I I ) Anarchic Melody...

Fore/word and Back/word _________ 3 The making of the distich : _____ 3 Characteristics: ______________ 3 Historical considerations: _____ 5 Types of Paradoxist distiches ___ 8 1. Clichés paraphrased: ___ 8 2. Parodies: _____________ 8 3. Reversed formulae: ____ 8 4. Double negation _______ 8 5. Double affirmation, ____ 8 6. Turn around on false tracks: _________________ 8 7. Hyperboles (exaggerated): __________________ 8 8. With nuance changeable from the title: ________ 8 9. Epigrammatic: ________ 8 10. Pseudo-paradoxes: ___ 8 11. Tautologies: ________ 9 12. Redundant: _________ 9 13. Based on pleonasms: _ 9 14. or on anti-pleonasms: 9 15. Substitution of the attribute in collocations ___ 9 16. Substitution of the complement in collocations 9 17. Permutation of various parts of the whole: ___ 9 18. The negation of the clichés ______________ 10 19. Antonymization (substantively, adjectively, etc.) ________________ 10 20. Fable against the grain: _________________ 10 21. Change in grammatical category (preserving substitutions’ homonymy): ________________ 10 22. Epistolary or colloquia style: _________...

Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed and humbled, can spring forth only from an unshackled mind combined with a willingness to imagine beyond the boundaries imposed by that ossified authority by which science inevitably becomes, as history teaches us, barren and decrepit. Revealing the secrets of Nature, so that we truly see ‘the sunlit plains extended, and at night the wondrous glory of the everlasting stars’*, requires far more than mere technical ability and mechanical dexterity learnt from books and consensus. The dustbin of scientific history is replete with discredited consensus and the grand reputations of erudite reactionaries. Only by boldly asking questions, fearlessly, despite opposition, and searching for answers where most have not looked for want of courage and independence of thought, can one hope to discover for one’s self. From nothing else can creativity blossom and grow, and without which the garden of science can o...

After the experiments were completed, the life span of such “atoms” was calculated theoretically in Chapiro’s works [61,62,63]. His main idea was that nuclear forces, acting between nucleon and anti-nucleon, can keep them far away from each other, hindering their annihilation. For instance, a proton and anti-proton are located at the opposite side of the same orbit and move around the orbit’s centre. If the diameter of their orbit is much larger than the diameter of the “annihilation area”, they can be kept from annihilation (see fig. 3). But because the orbit, according to Quantum Mechanics, is an actual cloud spreading far around the average radius, at any radius between the proton and the anti-proton there is a probability that they can meet one another at the annihilation distance. Therefore the nucleon---anti-nucleon system annihilates in any case, as this system is unstable by definition having a life span no more than 10-20 sec....

...me 26 2.7. Magic square problem 27 2.8. Palindromic number and iteration 27 2.9. Non-Euclidean geometry by giving up its fifth postulate 28 2.10. Smarandache Geometry and Degree of Negation in Geometries 28 2.11. Non-Archimedean triangle theorem 33 2.12. The cubic Diophantine equation 33 2.13. Multispaces and applications in physics 34 3 Unsolved Problems in Astrop...

Etymologically, aphorism + floral = aph(L)orism, which is a short reflection written on a floral design, or a short poetry accompanied by an artistic background. They are colorful contemplations. Maximus in minimis (Lat.) means very much in very little [max in min], or condensed thought, or ideating essence. They are actually maxims, adages, sayings mostly in one line (uni-stich) with a title, as a metaphoric statement, a breathing momentum that oils our soul....

Nonchalantly : The wind with its mantle steps lightly. Skin Condition : The Sun has spots too. At what time? When it rains, God cries. Atmosphere : Blue, as the sky dirtied by clouds. Bright : A balcony full of Sun. Natural disaster : The swans look drunk on the fetid lake. Surprisingly : The crow is a beautiful black. Elegant woman : A bird high on her legs. Most powerful chess piece : You are a queen but only in the dark. Medicinal plant : You’re a flower but amongst weeds. Force that attracts food : The stomach’s gravitation pulls me to food....

Passion.......................................................................23 Worthless.....................................................................23 Tired of you....................................................................23 Tittle-tattle....................................................................23 Talk is cheep...................................................................24 Give the man what he doesn’t have.................................................24 Novel for (non) writers...........................................................24 Desolate......................................................................24 Did I have the pleasure...........................................................24 Sloppy work....................................................................25 Despicable.....................................................................25 Wanted.......................................................................25 Talking in vain..................................................................25 Use caplets.....................................................

The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors...

This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical method to extrapolate such critical limit to primary tumour volume. Our model does not involve any physiological variables but rather is entirely based on time series observations of increase in primary tumour volume from the point of initial detection to the actual detection of metastases....

.......................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin Smarandache..15 2. On Recent Discovery of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in A...

The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors...

This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical method to extrapolate such critical limit to primary tumour volume. Our model does not involve any physiological variables but rather is entirely based on time series observations of increase in primary tumour volume from the point of initial detection to the actual detection of metastases....

.......................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin Smarandache..15 2. On Recent Discovery of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in A...

科学面临的难题 _ 中智学为何诞生 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以解决当今认知科学、信息科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通过新型开放模式改造当今各自然科 与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还属空白, 故借 对学科正式命名并引入中国。...

中智学, 新的哲学分支 _(Neutrosophy - A New Branch of Philosophy) 摘要: 本文推出了一个新的哲学分支, 中智学 _(neutrosphy), 研究中性的起源、本质和范畴以及和不同思想观念的作用。它的基本点是: 任何观念具有T%的真实性、I%的不确定性以及 的谬误性, 其中T, I, F为╟-0, 1+╢的标准或非标准子集。 _基本理论:任何观念 _ 趋于被 _ 所中和、削弱和平衡 _(不仅仅是被黑格尔主 的), 达到一种平衡状态。 中智学是中智逻辑学 _(在模糊逻辑的基础上总结出来的多值逻辑)、中智集合论 _(模糊 合论的概括总结)、中智概率论和中智统计学 _(分别是经典及非精确概率论、统计学的概括 结) 的基础。 _ 关键字与短语: 非标准分析, 超实数, 无穷小, 单子, 非标准实数单位区间, 集合运算。 _...

译者序 _Preface by the Translator ........................................5 作者简介 _Author’s Biography ..........................................9 译者简介 _Biography of the Translator.................................12 原书前言 _查尔斯·李 _.....................................................19 Preface by Charles T. Le 0．引言: 非标准实数单位区间 _.......................................24 Introduction: The Non-Standard Real Unit Interval 1．中智学——哲学的崭新分支 _.......................................27 Neutrosophy - a new branch of philosophy 2．中智逻辑——逻辑学的统一 _........................................90 Neutrosophic Logic - a unifying field in logics 3．中智集合论——集合论的统一 _....................................109 Neutrosophic Set - a unifying field in sets 4．中智概率论 _..........................................................113 ——传统概率论和非精确概率论的概括总结 _ ——以及中智统计学 _ Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics 附录: 中智学产生的定义 _..............................................117 Addenda: Definitions derived from Neutrosophics...

1. 科学面临的难题 中智学为何诞生 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学 艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以 决当今认知科学、信息 科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通 新型开放模式改造当今 各自然科学与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还 空白, 故借此对学科正式 命名并引入中国。...

中智学, 新的哲学分支(Neutrosophy - A New Branch of Philosophy) 摘要: 本文推出了一个新的哲学分支, 中智学 (neutrosphy), 研究中性的起源、本质和范畴以及和不同思想观念的 作用。它的基本点是: 任何观念具有T%的真实性、I%的不确定性以及 F%的谬误性, 其中T, I, F 为╟-0, 1+╢的标准或 非标准子集。 基本理论:任何观念 趋于被 所中和、削弱和平衡 (不仅仅是被黑格尔主张的), 达到一种 平衡状态。 中智学是中智逻辑学 (在模糊逻辑的基础上总结出来的多值逻辑)、中智集合论 (模糊集合论的概括总结)、中智概 率论和中智统计学 (分别是经典及非精确概率论、统计学的概括总结) 的基础。 关键字与短语: 非标准分析, 超实数, 无穷小, 单子, 非标准实数单位区间, 集合运算。...

译者序 Preface by the Translator ..................................5 作者简介 Author’s Biography ..............................9 译者简介 Biography of the Translator...........................12 原书前言 查尔斯·李 ............................................18 Preface by Charles T. Le 0．引言: 非标准实数单位区间 ..............................23 Introduction: The Non-Standard Real Unit Interval 1．中智学——哲学的崭新分支 ..............................26 Neutrosophy - a new branch of philosophy 2．中智逻辑——逻辑学的统一 ...............................83 Neutrosophic Logic - a unifying field in logics 3．中智集合论——集合论的统一 ..............................100 Neutrosophic Set - a unifying field in sets 4．中智概率论 ...........................................103 ——传统概率论和非精确概率论的概括总结 ——以及中智统计学 Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics 附录: 中智学产生的定义 ..................................106 Addenda: Definitions derived from Neutrosophics...

...c to the General Theory of Relativity to obtain a generalisation of Einstein’s four dimensional pseudo-Riemannian differentiable manifold in terms of Smarandache Geometry (Smarandache manifolds), by which new classes of relativistic particles and non-quantum teleportation are developed....

1.2 The basics of neutrosophy Neutrosophy studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. It considers that every idea tends to be neutralized, balanced by ideas; as a state of equilibrium. Neutrosophy is the basis of neutrosophic logic, neutrosophic set which generalizes the fuzzy set, and of neutrosphic probability and neutrosophic statistics, which generalize the classical and imprecise probability and statistics respectively. Neutrosophic Logic is a multiple-valued logic in which each proposition is estimated to have percentages of truth, indeterminacy, and falsity in T, I, and F respectively, where T, I, F are standard or non-standard subsets included in the non-standard unit interval ] −0, 1+[. It is an extension of fuzzy, intuitionistic, paraconsistent logics. ...

Preface of the Editor 4 Chapter 1 PROBLEM STATEMENT . THE BASICS OF NEUTROSOPHY 1.1 Problem statement 5 1.2 The basics of neutrosophy 8 1.3 Neutrosophic subjects 13 1.4 Neutrosophic logic. The origin of neutrosophy 14 1.5 Definitions of neutrosophic 16 Chapter 2 TRAJECTORIES AND PARTICLES 2.1 Einstein’s basic space-time 18 2.2 Standard set of trajectories and particles. A way to expand the set 22 2.3 Introducing trajectories of mixed isotropic/non-isotropic kind 28 2.4 Particles moving along mixed isotropic/non-isotropic trajectories 31 2.5 S-denying the signature conditions. Classification of the expanded spaces 35 2.6 More on an expanded space-time of kind IV 45 2.7 A space-time of kind IV: a home space for virtual photons 52 2.8 A space-time of kind IV: non-quantum teleportation of photons 55 2.9 Conclusions 59 Chapter 3 ENTANGLED STATES AND QUANTUM CAUSALITY THRESHOLD 3.1 Disentangled and entangled particles in General Relativity. Problem statement 61 3.2 Incorporating entangled states into General Relativity 64 3.3 Quantum Causality Threshold in General Relativity 69 3.4 Conclusions 72 Biblio...

This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given....

2 Lukasiewicz Multi-Valued-logic: History and Introduction to Multi- Valued Algebra 2.1 Introduction to trivalent logic and plurivalent logic We all have heard of typical binary logic, Yes or No. Or in a famous phrase by Shakespeare: “To be or not to be.” In the same way all computer hardwares from early sixties up to this year are built upon the same binary logic. It is known that the Classical Logic, also called Bivalent Logic for taking only two values {0, 1}, or Boolean Logic from British mathematician George Boole (1815-64), was named by the philosopher Quine (1981) “sweet simplicity.” [57] But this typical binary logic is not without problems. In the light of aforementioned ‘garment analogue’, we can compare this binary logic with a classic black-and-white tuxedo. It is timeless design, but of course you will not wear it for all occasions. Aristotle himself apparently knew this problem; therefore he introduced new terms ‘contingency’ and ‘possibility’ into his modal logic [5]. And then American logician Lewis first formulated these concepts of logical modality. ...

Contents Foreword 6 1 Introduction: Paradoxes, Lukasiewicz, Multi-Valued logic 7 2 Lukasiewicz Multi-Valued Logic: History and Introduction to Multi-Valued Algebra 10 2.1. Introduction to trivalent logic and plurivalent logic 10 2.2. History of Lukasiewicz and Multi-Valued Logic 12 2.3. Introduction to Multi-Valued Algebra, Chang’s Notation 15 2.4. Linkage between Multi-Valued Logic and Quantum Mechanics 15 2.5. Exercise 17 3 Neutrosophy 25 3.1. Introduction to Neutrosophy 25 3.2. Introduction to Non-Standard Analysis 26 3.3. Definition of Neutrosophic Components 27 3.4. Formalization 28 3.5. Evolution of an Idea 30 3.6. Definition of Neutrosophic Logic 31 3.7. Differences between Neutrosophic Logic and IFL 32 3.8. Operations with Sets 33 3.9. Generalizations 34 4 Schrödinger Equation 39 4.1. Introduction 39 4.2. Quantum wave dynamics and classical dynamical system 43 4.3. A new derivation of Schrödinger-type Equation 45 5 Solution to Schrödinger’s Cat Paradox 47 5.1. Standard interpretation 47 5.2. Schrödinger’s Cat Paradox 48 5.3. Hidden-variable hypothesis 50 5.4. Hydrodynamic viewpoint and diffusion i...

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....

...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...

...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...

...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 ...

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....

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. ...

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...

...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...

...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 . . . . ....