A New Approach to Quantum Logic

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

Publisher: N.A

ISBN: 9781904987536

Category: Mathematics

Page: 182

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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.
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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

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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.
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Essays in Logic and Ontology

Author: Jacek Malinowski,Andrzej Pietruszczak

Publisher: Rodopi

ISBN: 9042021306

Category: Philosophy

Page: 400

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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.
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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

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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.
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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

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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.
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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

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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
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Logic in Reality

Author: JOSEPH BRENNER

Publisher: Springer Science & Business Media

ISBN: 1402083750

Category: Philosophy

Page: 362

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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.
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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

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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.
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