A New Approach to Quantum Logic

Author: Kurt Engesser,Dov M. Gabbay,Daniel Lehmann

Publisher: N.A

ISBN: 9781904987536

Category: Mathematics

Page: 182

View: 5729

This monograph is an investigation into certain new logical structures implicit in the formalism of quantum mechanics. Its message rests on two pillars. The first pillar is the dynamic view of propositions. Propositions are viewed as acting on states of the world and changing them rather than just being true or false in them. The second pillar is a logical enquiry into the nature of the states of a dynamic framework in general and thus the nature of physical states in particular. It turns out that a physical state viewed as a logical entity must encode other states and also itself. The main logical structures under investigation are that of an M-algebra and that of a holistic logic. In a sense to be made precise the latter structures reflect the 'holistic' nature of quantum mechanics.
Release

Handbook of Quantum Logic and Quantum Structures

Quantum Structures

Author: Kurt Engesser,Dov M. Gabbay,Daniel Lehmann

Publisher: Elsevier

ISBN: 9780080550381

Category: Computers

Page: 818

View: 6755

Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled “The logic of quantum mechanics quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results. Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate. The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability. - Written by eminent scholars in the field of logic - A comprehensive presentation of the theory, approaches and results in the field of quantum logic - Volume focuses on quantum structures
Release

Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing

10th International Conference, RSFDGrC 2005, Regina, Canada, August 31 - September 3, 2005, Proceedings

Author: Dominik Slezak,Guoyin Wang,Marcin Szczuka,Ivo Duentsch,Yiyu Yao

Publisher: Springer Science & Business Media

ISBN: 3540286535

Category: Computers

Page: 742

View: 8665

The two volume set LNAI 3641 and LNAI 3642 constitutes the refereed proceedings of the 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, RSFDGrC 2005, held in Regina, Canada in August/September 2005. The 119 revised full papers presented were carefully reviewed and selected from a total of 277 submissions. They comprise the two volumes together with 6 invited papers, 22 approved workshop papers, and 5 special section papers that all were carefully selected and thoroughly revised. The first volume includes 75 contributions related to rough set approximations, rough-algebraic foundations, feature selection and reduction, reasoning in information systems, rough-probabilistic approaches, rough-fuzzy hybridization, fuzzy methods in data analysis, evolutionary computing, machine learning, approximate and uncertain reasoning, probabilistic network models, spatial and temporal reasoning, non-standard logics, and granular computing. The second volume contains 77 contributions and deals with rough set software, data mining, hybrid and hierarchical methods, information retrieval, image recognition and processing, multimedia applications, medical applications, web content analysis, business and industrial applications, the approved workshop papers and the papers accepted for a special session on intelligent and sapient systems.
Release

Essays in Logic and Ontology

Author: Jacek Malinowski,Andrzej Pietruszczak

Publisher: Rodopi

ISBN: 9042021306

Category: Philosophy

Page: 400

View: 7509

The aim of this book is to present essays centered upon the subjects of Formal Ontology and Logical Philosophy. The idea of investigating philosophical problems by means of logical methods was intensively promoted in Torun by the Department of Logic of Nicolaus Copernicus University during last decade. Another aim of this book is to present to the philosophical and logical audience the activities of the Torunian Department of Logic during this decade. The papers in this volume contain the results concerning Logic and Logical Philosophy, obtained within the confines of the projects initiated by the Department of Logic and other research projects in which the Torunian Department of Logic took part.
Release

Logic, Mathematics, Philosophy, Vintage Enthusiasms

Essays in Honour of John L. Bell

Author: David DeVidi,Michael Hallett,Peter Clark

Publisher: Springer Science & Business Media

ISBN: 9789400702141

Category: Philosophy

Page: 486

View: 324

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.
Release

Logic in Reality

Author: JOSEPH BRENNER

Publisher: Springer Science & Business Media

ISBN: 1402083750

Category: Philosophy

Page: 362

View: 5508

This book is both dif?cult and rewarding, affording a new perspective on logic and reality, basically seen in terms of change and stability, being and becoming. Most importantly it exemplifies a mode of doing philosophy of science that seems a welcome departure from the traditional focus on purely analytic arguments. The author approaches ontology, metaphysics, and logic as having offered a number of ways of constructing the description of reality, and aims at deepening their relationships in a new way. Going beyond the mere abstract and formal aspects of logical analysis, he offers a new architecture of logic that sees it as applied not only to the “reasoning processes” belonging to the first disciplinary group – ontology – but also directly concerned with en- ties, events, and phenomena studied by the second one – metaphysics. It is the task of the book to elaborate such a constructive logic, both by offering a lo- cal view of the structure of the reality in general and by proffering a wealth of models able to encompass its implications for science. In turning from the merely formal to the constructive account of logic Brenner overcomes the limitation of logic to linguistic concepts so that it can be not only a logic “of” reality but also “in” that reality which is constitutively characterized by a number of fundamental dualities (observer and observed, self and not-self, internal and external, etc.
Release

Current Research in Operational Quantum Logic

Algebras, Categories, Languages

Author: Bob Coecke,David Moore,Alexander Wilce

Publisher: Springer Science & Business Media

ISBN: 9401712018

Category: Science

Page: 325

View: 5703

The present volume has its origins in a pair of informal workshops held at the Free University of Brussels, in June of 1998 and May of 1999, named "Current Research 1 in Operational Quantum Logic". These brought together mathematicians and physicists working in operational quantum logic and related areas, as well as a number of interested philosophers of science, for a rare opportunity to discuss recent developments in this field. After some discussion, it was decided that, rather than producing a volume of conference proceedings, we would try to organize the conferees to produce a set of comprehensive survey papers, which would not only report on recent developments in quantum logic, but also provide a tutorial overview of the subject suitable for an interested non-specialist audience. The resulting volume provides an overview of the concepts and methods used in current research in quantum logic, viewed both as a branch of mathemati cal physics and as an area of pure mathematics. The first half of the book is concerned with the algebraic side of the subject, and in particular the theory of orthomodular lattices and posets, effect algebras, etc. In the second half of the book, special attention is given to categorical methods and to connections with theoretical computer science. At the 1999 workshop, we were fortunate to hear three excellent lectures by David J. Foulis, represented here by two contributions. Dave's work, spanning 40 years, has helped to define, and continues to reshape, the field of quantum logic.
Release

The New Physics and Cosmology

Dialogues with the Dalai Lama

Author: Arthur Zajonc

Publisher: Oxford University Press

ISBN: 0199882835

Category: Science

Page: 264

View: 2476

What happens when the Dalai Lama meets with leading physicists and a historian? This book is the carefully edited record of the fascinating discussions at a Mind and Life conference in which five leading physicists and a historian (David Finkelstein, George Greenstein, Piet Hut, Arthur Zajonc, Anton Zeilinger, and Tu Weiming) discussed with the Dalai Lama current thought in theoretical quantum physics, in the context of Buddhist philosophy. A contribution to the science-religion interface, and a useful explanation of our basic understanding of quantum reality, couched at a level that intelligent readers without a deep involvement in science can grasp. In the tradition of other popular books on resonances between modern quantum physics and Zen or Buddhist mystical traditions--notably The Dancing Wu Li Masters and The Tao of Physics, this book gives a clear and useful update of the genuine correspondences between these two rather disparate approaches to understanding the nature of reality.
Release

PSA 1974

Proceedings of the 1974 Biennial Meeting Philosophy of Science Association

Author: Robert S. Cohen,C.A. Hooker,Alex C. Michalos,J. van Evra

Publisher: Springer Science & Business Media

ISBN: 9401014493

Category: Science

Page: 747

View: 8433

For this book, we have selected papers from symposia and contributed sessions at the fourth biennial meeting of the Philosophy of Science Association, held at the University of Notre Dame on November 1-3, 1974. The meeting was lively and well-attended, and we regret that there was no way to record here the many stimulating discussions after the papers and during the informal hours. We also regret that we had in sufficient space for all the contributed papers. Even more, some of the symposia were not available: those on systems and decision theory (c. W. Churchman, P. Suppes, I. Levi), and on the Marxist philosophy of science (M. W. Wartofsky, R. S. Cohen, E. N. Hiebert). Unhappily several individual contributions to other symposia were likewise not available: I. Velikovsky in the session on his own work and the politics of science, D. Finkelstein in the session on quantum logic. Memorial minutes were read for Alan Ross Anderson (prepared by Nuel Belnap) and for Imre Lakatos (prepared by Paul Feyerabend). They initiate this volume of philosophy of science in the mid-seventies.
Release

Fuzzy Sets

Proceedings of the International Conference on Fuzzy Sets Theory and Its Applications, Liptovský Mikuláš, February 17-21, 1992

Author: Beloslav Riečan,Miloslav Duchoň

Publisher: N.A

ISBN: N.A

Category: Fuzzy sets

Page: 150

View: 844

Release

Hermeneutic Philosophy of Science, Van Gogh’s Eyes, and God

Essays in Honor of Patrick A. Heelan, S.J.

Author: B.E. Babich

Publisher: Springer Science & Business Media

ISBN: 9401717672

Category: Science

Page: 500

View: 2462

This richly textured book bridges analytic and hermeneutic and phenomenological philosophy of science. It features unique resources for students of the philosophy and history of quantum mechanics and the Copenhagen Interpretation, cognitive theory and the psychology of perception, the history and philosophy of art, and the pragmatic and historical relationships between religion and science.
Release

A Companion to the Philosophy of Time

Author: Adrian Bardon,Heather Dyke

Publisher: John Wiley & Sons

ISBN: 1118522052

Category: Philosophy

Page: 600

View: 5687

A Companion to the Philosophy of Time presents thebroadest treatment of this subject yet; 32 specially commissionedarticles - written by an international line-up of experts –provide an unparalleled reference work for students and specialistsalike in this exciting field. The most comprehensive reference work on the philosophy of timecurrently available The first collection to tackle the historical development ofthe philosophy of time in addition to covering contemporarywork Provides a tripartite approach in its organization, coveringhistory of the philosophy of time, time as a feature of thephysical world, and time as a feature of experience Includes contributions from both distinguished,well-established scholars and rising stars in the field
Release

K-theory and Noncommutative Geometry

Author: Guillermo Cortiñas

Publisher: European Mathematical Society

ISBN: 9783037190609

Category: K-theory

Page: 440

View: 4320

"Contains the proceedings of VASBI, the ICM 2006 satellite on K-theory and Noncommutative Geometry which took place in Valladolid, Spain, from August 31 to September 6, 2006."--Pref.
Release

Approximability of Optimization Problems through Adiabatic Quantum Computation

Author: William Cruz-Santos,Guillermo Morales-Luna

Publisher: Morgan & Claypool Publishers

ISBN: 1627055576

Category: Science

Page: 113

View: 8190

The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is large enough, then the system remains close to its ground state. An AQC algorithm uses the adiabatic theorem to approximate the ground state of the final Hamiltonian that corresponds to the solution of the given optimization problem. In this book, we investigate the computational simulation of AQC algorithms applied to the MAX-SAT problem. A symbolic analysis of the AQC solution is given in order to understand the involved computational complexity of AQC algorithms. This approach can be extended to other combinatorial optimization problems and can be used for the classical simulation of an AQC algorithm where a Hamiltonian problem is constructed. This construction requires the computation of a sparse matrix of dimension 2n × 2n, by means of tensor products, where n is the dimension of the quantum system. Also, a general scheme to design AQC algorithms is proposed, based on a natural correspondence between optimization Boolean variables and quantum bits. Combinatorial graph problems are in correspondence with pseudo-Boolean maps that are reduced in polynomial time to quadratic maps. Finally, the relation among NP-hard problems is investigated, as well as its logical representability, and is applied to the design of AQC algorithms. It is shown that every monadic second-order logic (MSOL) expression has associated pseudo-Boolean maps that can be obtained by expanding the given expression, and also can be reduced to quadratic forms. Table of Contents: Preface / Acknowledgments / Introduction / Approximability of NP-hard Problems / Adiabatic Quantum Computing / Efficient Hamiltonian Construction / AQC for Pseudo-Boolean Optimization / A General Strategy to Solve NP-Hard Problems / Conclusions / Bibliography / Authors' Biographies
Release

Quantum Cosmology Research Trends

Author: Albert Reimer

Publisher: Nova Publishers

ISBN: 9781594543203

Category: Science

Page: 201

View: 7971

Quantum Cosmology Research Trends - Horizons in World Physics
Release

On the Logos: A Naïve View on Ordinary Reasoning and Fuzzy Logic

Author: Enric Trillas

Publisher: Springer

ISBN: 3319560530

Category: Computers

Page: 213

View: 4184

This book offers an inspiring and naïve view on language and reasoning. It presents a new approach to ordinary reasoning that follows the author’s former work on fuzzy logic. Starting from a pragmatic scientific view on meaning as a quantity, and the common sense reasoning from a primitive notion of inference, which is shared by both laypeople and experts, the book shows how this can evolve, through the addition of more and more suppositions, into various formal and specialized modes of precise, imprecise, and approximate reasoning. The logos are intended here as a synonym for rationality, which is usually shown by the processes of questioning, guessing, telling, and computing. Written in a discursive style and without too many technicalities, the book presents a number of reflections on the study of reasoning, together with a new perspective on fuzzy logic and Zadeh’s “computing with words” grounded in both language and reasoning. It also highlights some mathematical developments supporting this view. Lastly, it addresses a series of questions aimed at fostering new discussions and future research into this topic. All in all, this book represents an inspiring read for professors and researchers in computer science, and fuzzy logic in particular, as well as for psychologists, linguists and philosophers.
Release