Matrix Logic
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Matrix Logic
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Author : A. Stern
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Matrix Logic written by A. Stern and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
In this pioneering work, the author develops a fundamental formulation of logic in terms of theory of matrices and vector spaces. The discovery of matrix logic represents a landmark in the further formalization of logic. For the first time the power of direct mathematical computation is applied to the whole set of logic operations, allowing the derivation of both the classical and modal logics from the same formal base.The new formalism allows the author to enlarge the alphabet of the truth-values with negative logic antivalues and to link matrix logic descriptions with the Dirac formulation of quantum theory - a result having fundamental implications and repercussions for science as a whole.As a unified language which permits a logical examination of the underlying phenomena of quantum field theory and vice versa, matrix logic opens new avenues for the study of fundamental interactions and gives rise to a revolutionary conclusion that physics as such can be viewed and studied as a logic in the fundamental sense.Finally, modelling itself on exact sciences, matrix logic does not refute the classical logic but instead incorporates it as a special deterministic limit. The book requires multidisciplinary knowledge and will be of interest to physicists, mathematicians, computer scientists and engineers.
Matrix Logic And Mind
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Author : A. Stern
language : en
Publisher: Elsevier
Release Date : 1992-02-12
Matrix Logic And Mind written by A. Stern and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-12 with Mathematics categories.
In this revolutionary work, the author sets the stage for the science of the 21st Century, pursuing an unprecedented synthesis of fields previously considered unrelated. Beginning with simple classical concepts, he ends with a complex multidisciplinary theory requiring a high level of abstraction. The work progresses across the sciences in several multidisciplinary directions: Mathematical logic, fundamental physics, computer science and the theory of intelligence. Extraordinarily enough, the author breaks new ground in all these fields. In the field of fundamental physics the author reaches the revolutionary conclusion that physics can be viewed and studied as logic in a fundamental sense, as compared with Einstein's view of physics as space-time geometry. This opens new, exciting prospects for the study of fundamental interactions. A formulation of logic in terms of matrix operators and logic vector spaces allows the author to tackle for the first time the intractable problem of cognition in a scientific manner. In the same way as the findings of Heisenberg and Dirac in the 1930s provided a conceptual and mathematical foundation for quantum physics, matrix operator logic supports an important breakthrough in the study of the physics of the mind, which is interpreted as a fractal of quantum mechanics. Introducing a concept of logic quantum numbers, the author concludes that the problem of logic and the intelligence code in general can be effectively formulated as eigenvalue problems similar to those of theoretical physics. With this important leap forward in the study of the mechanism of mind, the author concludes that the latter cannot be fully understood either within classical or quantum notions. A higher-order covariant theory is required to accommodate the fundamental effect of high-level intelligence. The landmark results obtained by the author will have implications and repercussions for the very foundations of science as a whole. Moreover, Stern's Matrix Logic is suitable for a broad spectrum of practical applications in contemporary technologies.
Topics In Engineering Logic
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Author : Morton Nadler
language : en
Publisher: Elsevier
Release Date : 2014-06-20
Topics In Engineering Logic written by Morton Nadler and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-20 with Technology & Engineering categories.
Topics in Engineering Logic contains the lectures given at the Indian Statistical Institute in Calcutta, India, during the Spring of 1959. The lectures focus on a variety of topics related to engineering logic, including the use of the logical matrix as an auxiliary to the construction of various types of codes. Elementary logical circuits for synchronous systems are also considered, with emphasis on "two-wire" systems based on static flip-flops and having various phase structures. Comprised of seven chapters, this volume begins with an introduction to the logical matrix, a form of representation of logical functions that permits rapid and clear solution of varied problems in logical design. The discussion then turns to elementary logical circuits for synchronous systems and their physical properties, with particular reference to contacts, diodes, and transistors as well as phase structures and diode-gated flip-flops for single-phase and two-phase applications. Subsequent chapters deal with a graphical approach based on the logical matrix as a method for reducing the canonic form to the two-level minimal form; codes and matrices; operational circuits; and the question of increasing reliability through structural redundance. The book concludes with several typical logical design problems, including a drum-indexing circuit and a series-parallel decimal multiplier. This monograph will be of interest to engineers.
More Math Logic Mysteries
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Author : Marilynn L. Rapp Buxton
language : en
Publisher: Taylor & Francis
Release Date : 2021-09-03
More Math Logic Mysteries written by Marilynn L. Rapp Buxton and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-03 with Education categories.
Students love trying to solve challenging puzzles. So, why not build and review their math skills while they're having fun? More Math Logic Mysteries, the sequel to the best-selling Math Logic Mysteries, requires students to complete math problems and use deductive reasoning to unlock the clues needed to solve matrix-based logic problems. Mathematical skills covered include measurement, number operations, geometry, probability, fractions, decimals, percentages, and algebra. The puzzles range from simple introductions to matrix-based problems, to more difficult puzzles that cover advanced math topics. Each reproducible puzzle is based on an enjoyable story your students will love as they attempt to solve problems and crack the mysteries. This book includes a detailed how-to section for teaching logic puzzles and an in-depth answer key, so students can understand the thinking process behind each solution. After doing these fun and challenging puzzles, your students will ask for even More Math Logic Mysteries! Grades 5-8
Intellectics And Computational Logic
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Author : Steffen Hölldobler
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Intellectics And Computational Logic written by Steffen Hölldobler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Philosophy categories.
`Intellectics' seeks to understand the functions, structure and operation of the human intellect and to test artificial systems to see the extent to which they can substitute or complement such functions. The word itself was introduced in the early 1980s by Wolfgang Bibel to describe the united fields of artificial intelligence and cognitive science. The book collects papers by distinguished researchers, colleagues and former students of Bibel's, all of whom have worked together with him, and who present their work to him here to mark his 60th birthday. The papers discuss significant issues in intellectics and computational logic, ranging across automated deduction, logic programming, the logic-based approach to intellectics, cognitive robotics, knowledge representation and reasoning. Each paper contains new, previously unpublished, reviewed results. The collection is a state of the art account of the current capabilities and limitations of a computational-logic-based approach to intellectics. Readership: Researchers who are convinced that the intelligent behaviour of machines should be based on a rigid formal treatment of knowledge representation and reasoning.
Dictionary Of Logic As Applied In The Study Of Language
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Author : W. Marciszewski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Dictionary Of Logic As Applied In The Study Of Language written by W. Marciszewski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Philosophy categories.
1. STRUCTURE AND REFERENCES 1.1. The main part of the dictionary consists of alphabetically arranged articles concerned with basic logical theories and some other selected topics. Within each article a set of concepts is defined in their mutual relations. This way of defining concepts in the context of a theory provides better understand ing of ideas than that provided by isolated short defmitions. A disadvantage of this method is that it takes more time to look something up inside an extensive article. To reduce this disadvantage the following measures have been adopted. Each article is divided into numbered sections, the numbers, in boldface type, being addresses to which we refer. Those sections of larger articles which are divided at the first level, i.e. numbered with single numerals, have titles. Main sections are further subdivided, the subsections being numbered by numerals added to the main section number, e.g. I, 1.1, 1.2, ... , 1.1.1, 1.1.2, and so on. A comprehensive subject index is supplied together with a glossary. The aim of the latter is to provide, if possible, short defmitions which sometimes may prove sufficient. As to the use of the glossary, see the comment preceding it.
Proceedings Of The First International Conference On Neutrosophy Neutrosophic Logic Neutrosophic Set Neutrosophic Porbability And Statistics
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Author : Florentin Smarandache editor
language : en
Publisher: Infinite Study
Release Date : 2003-01-01
Proceedings Of The First International Conference On Neutrosophy Neutrosophic Logic Neutrosophic Set Neutrosophic Porbability And Statistics written by Florentin Smarandache editor and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
Collected papers on neutrosophics [such as: ?neutrosophy? - a new branch of philosophy, ?neutrosophic logic? ? a generalization of the fuzzy logic, ?neutrosophic set? ? a generalization of the fuzzy set, and ?neutrosophic probability? ? a generalization of classical probability and imprecise probability] by Florentin Smarandache, Jean Dezert, Andrzej Buller, Mohammad Khoshnevisan, Sarjinder Singh, Sukanto Bhattacharya, Feng Liu, Gh. C. Dinulescu-Campina, Chris Lucas, and Carlos Gershenson.Neutrosophic Logic involved the foundation of the Dezert-Smarandache Theory of Plausible and Paradoxical Reasoning, which has taken into consideration the combination of uncertain and contradictory information, used now in artificial intelligence.
Modal Logic
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Author : Nino B. Cocchiarella
language : en
Publisher: Oxford University Press
Release Date : 2008-08-04
Modal Logic written by Nino B. Cocchiarella and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-04 with Mathematics categories.
In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight. All of the S1-S5 modal logics of Lewis and Langford, among others, are constructed. A matrix, or many-valued semantics, for sentential modal logic is formalized, and an important result that no finite matrix can characterize any of the standard modal logics is proven. Exercises, some of which show independence results, help to develop logical skills. A separate sentential modal logic of logical necessity in logical atomism is also constructed and shown to be complete and decidable. On the first-order level of the logic of logical necessity, the modal thesis of anti-essentialism is valid and every de re sentence is provably equivalent to a de dicto sentence. An elegant extension of the standard sentential modal logics into several first-order modal logics is developed. Both a first-order modal logic for possibilism containing actualism as a proper part as well as a separate modal logic for actualism alone are constructed for a variety of modal systems. Exercises on this level show the connections between modal laws and quantifier logic regarding generalization into, or out of, modal contexts and the conditions required for the necessity of identity and non-identity. Two types of second-order modal logics, one possibilist and the other actualist, are developed based on a distinction between existence-entailing concepts and concepts in general. The result is a deeper second-order analysis of possibilism and actualism as ontological frameworks. Exercises regarding second-order predicate quantifiers clarify the distinction between existence-entailing concepts and concepts in general. Modal Logic is ideally suited as a core text for graduate and undergraduate courses in modal logic, and as supplementary reading in courses on mathematical logic, formal ontology, and artificial intelligence.
The Road To Universal Logic
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Author : Arnold Koslow
language : en
Publisher: Birkhäuser
Release Date : 2015-06-10
The Road To Universal Logic written by Arnold Koslow and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-10 with Mathematics categories.
This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert). The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade. These essays will be of interest to all students and researchers interested in the nature and future of logic.
Initiatives In Logic
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Author : Jan J.T. Srzednicki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Initiatives In Logic written by Jan J.T. Srzednicki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Philosophy categories.