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The Monograph introduces the Optical implementation of quantum computation. It proposes a new scheme of implementing the qubit using electromagnetic modes in a waveguide and realizes some elementary logic functions associated to quantum computing. The designed logic gates were also verified using the "Beam Propagation Method". The Deutsch Algorithm has been simulated using the designed logic gates. Finally the NOT gate implementation was experimentally demonstrated.
An enlightening introduction to the study of logic: its history, philosophical foundations, and formal structures Logic: Inquiry, Argument, and Order is the first book of its kind to frame the study of introductory logic in terms of problems connected to wider issues of knowledge and judgment that arise in the context of racial, cultural, and religious diversity. With its accessible style and integration of philosophical inquiry and real-life concerns, this book offers a novel approach to the theory of logic and its relevance to questions of meaning and value that arise in the world around us. The book poses four problems for logic: Is logic separate from experience? Does logic require dualisms? Can logic reconcile opposed ways of understanding the world? And when things are divided, does the boundary have a logic? The author begins the exploration of these questions with a discussion of the process of analyzing and constructing arguments. Using the logical theories of C. S. Peirce, John Dewey, and Josiah Royce to frame the investigation, subsequent chapters outline the process of inquiry, the concept of communicative action, the nature of validity, categorical reasoning through the theory of the syllogism, and inductive reasoning and probability. The book concludes with a presentation of modal logic, propositional logic, and quantification. Logic is presented as emerging from the activities of inquiry and communication, allowing readers to understand even the most difficult aspects of formal logic as straightforward developments of the process of anticipating and taking action. Numerous practice problems use arguments related to issues of diversity and social theory, and the book introduces methods of proving validity that include Venn diagrams, natural deduction, and the method of tableaux. Logic: Inquiry, Argument, and Order is an ideal book for courses on philosophical methods and critical reasoning at the upper-undergraduate and graduate levels. It is also an insightful reference for anyone who would like to explore a cross-cultural approach to the topic of logic.
This work investigates the Logic that permeates our talk exchanges, that normally fall in the realm of Pragmatics. Two linguistic phenomena are specifically investigated in this dissertation: scalar implicatures and donkey anaphora. At first glance, these seem two distant, unrelated phenomena. At a closer look, however, they reveal some similarities that are specifically addressed and highlighted in this dissertation. In particular, the experimental findings discussed here converge on the revelation of a general interpretative strategy, which is captured in the title of this work: in our ordinary conversations, we seem to appeal to Logic consistently. This, in turn, suggests a more systematic way to analyze, even experimentally, the way we deal with the interpretation of pronouns or the computation of pragmatic inferences in our ordinary conversations, revealing Logic underneath Pragmatics.
Over the past half century wires and logic gates in computers have halved in size every year and a half, creating a phenomenon known as the Moore’s law. As the size of computer components reduces towards the atomic scale, however, the classical laws of thermodynamics are no longer able to predict the real behavior of electronic devices. In this context, the theory of quantum mechanics becomes increasingly important to characterize how circuits operate. Quantum information is the theory of communication and computation born to study the potential arising from information encoded in elementary particles, such as photons. The essential goal of quantum information is to determine how the quantum laws ruling the peculiar phenomena happening at an atomic scale can be used to enhance the capabilities of computers and communication systems.
There is no other entity of mathematics which had witnessed naming ceremony than the numbers. They have been called objects, classes, sets, and types, to name a few. What these names as numbers have in common is the exclusion of space from numbers. The result is the dichotomy of numbers and things. What this means in the end is the imposition of one on the other. This dichotomy fits in with the law of Excluded Middle which is central to the foundations of traditional mathematics and the sciences. Now what happens where Space is included in Number, not as an object, but as a Figure with the Identity that they share inbetween? What we got is a breathing, living world as a spacefigure. The fluid logic numbers of transfigural mathematics, are a flow of One in the Other of Nature and the World and these Other, as a flow in All. Every fluid logic number as a figure, covering human beings, trees, the seas, birds, the flora and fauna, and the universe, is included in Space - natural, social, cultural etc - and Space is included in it, also as figure. Inbetween them is Identity with which, together, they make a fluid logic number. This is the core of Transfigural Logic of Included Other.
Relative-Fuzzy is a new approach for handling the complex ambiguity type of uncertainty that may exist in data, for software engineering of predictive Data Mining (DM) classification models. This approach is based on a novel type of fuzzy logic which has been called Relative-Fuzzy Logic (RFL). RFL defines a new formulation of the problem of ambiguity type of uncertainty in terms of States Of Proposition (SOP). RFL describes its membership (semantic) value by using the new definition of Domain of Proposition (DOP), which is based on the relativity principle as defined by possible-worlds logic. Two types of logic; namely fuzzy logic and possible-world logic, have been mixed to produce a new membership value set that is able to handle fuzziness and multiple viewpoints at the same time, which called Relative-Fuzzy membership value set. For implementation purpose, a new architecture of Hierarchical Neural Network (HNN) called ML/RFL-Based Net along with its new learning and recalling algorithms has been developed. This new type of HNN is considered to be a RFL computation based machine.
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twelfth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association of Symbolic Logic, held at the University of the Basque Country, San Sebastian in July 1996. The main topics were model theory, proof theory, recursion and complexity theory, models of arithmetic, logic for artificial intelligence, formal semantics of natural language, and philosophy of contemporary logic. The volume includes eleven papers from pre-eminent researchers in mathematical logic.
Grobner bases are the single most important tool in applicable algebraic geometry. This is in part because they can be used to solve systems of polynomial equations. Applications in science and technology are abundant, particularly in cryptography and coding theory. Grobner bases computation is challenging and a great deal of effort has been devoted to improve algorithms to compute faster larger bases. The concept of mutant polynomials, introduced by Ding in 2006, characterizes a phenomenon of degeneration in the process of Grobner bases computation. Exploiting the appearance of mutant polynomials has led to significant improvements in Grobner bases Computation. In this work we describe several such improvements and we establish some theoretical results for mutant polynomials. We also propose LASyz, a method to avoid redundant computation in Grobner bases computation that is compatible with mutant algorithms. This is achieved by simple linear algebra procedures used to compute generators for the module of syzygies. Overall, this book provides an introduction to the state-of-the-art in Grobner bases computation together with the first steps towards a theory of mutant polynomials.
Originally published in 1914, this book presents an exposition of the elementary principles of logic. The text is divided into two main parts. The first part discusses the older system of logic, defined, in this context, as 'a carefully limited subject to get up for an elementary examination'. The second part discusses the modern system of logic, defined as 'a free study of some of the chief risks of error in reasoning'. Notes are incorporated throughout. This book will be of value to anyone with an interest in logic and philosophy.
Although it is one which has inspired fierce decade in the recent past, the question of the return of cultural objects is not a new one. This important book explores the removal and the return of cultural objects from occupied communities from the nineteenth century to the twentieth century and explores the concurrent evolution of international cultural heritage law. Examining the responses of governments and of museums to the question of restitution, this book is essential reading for archaeologists, international lawyers and all those involved in cultural resource management.
Arrangements of superconducting islands interspersed by Josephson junctions hold an enormous potential for the future of quantum and classical computation, sensing and metamaterials. Here we describe possible vortex quantum bits that have their design based upon Josephson technologies. The Josephson qubits are analogous to artificial atoms and exhibit clearly definable energy levels that are a function of the number of vortex states in a system and the applied magnetic flux. We describe these energies and a method to very accurately obtain them. We discuss quantum gates and algorithms that can be used for logic operations, entanglement, and also adiabatic quantum computing. The technologies being developed for quantum computation also have the potential for use in other applications, such as quantum sensing and metamaterials, and these topics run in parallel throughout the text.
The main part of the book is a comprehensive overview of the development of fuzzy logic and its applications in various areas of human affair since its genesis in the mid 1960s. This overview is then employed for assessing the significance of fuzzy logic and mathematics based on fuzzy logic.
The Economy of Prestige – Prizes, Awards, and the Circulation of Cultural Value