Current Research in Operational Quantum Logic

1. Front Matter

   Pages I-VII

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2. Introduction

   1. Operational Quantum Logic: An Overview

      • Bob Coecke, David Moore, Alexander Wilce

      Pages 1-36

3. Algebras

   1. Algebraic Aspects of Orthomodular Lattices

      • Gunter Bruns, John Harding

      Pages 37-65

   2. Observables in the Logico-Algebraic Approach

      • Pavel Pták

      Pages 67-80

   3. Test Spaces and Orthoalgebras

      • Alexander Wilce

      Pages 81-114

   4. Representations on Unigroups

      • David J. Foulis

      Pages 115-138

   5. Free Extensions of Group Actions, Induced Representations, and the Foundations of Physics

      • David J. Foulis, Alexander Wilce

      Pages 139-165

4. Categories

   1. Short Introduction to Enriched Categories

      • Francis Borceux, Isar Stubbe

      Pages 167-194

   2. Operational Galois Adjunctions

      • Bob Coecke, David Moore

      Pages 195-218

   3. Operational Axiomatics and Compound Systems

      • Frank Valckenborgh

      Pages 219-244

   4. Quantales

      • Jan Paseka, Jiří Rosický

      Pages 245-262

5. Languages

   1. Quantales and Observational Semantics

      • Pedro Resende

      Pages 263-288

   2. Quantum Languages

      • Stan Gudder

      Pages 289-310

6. Back Matter

   Pages 311-325

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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.

• Lattice
• Mathematica
• algebra
• computer science
• group action
• logic
• semantics

• Department of Mathematics, FUND, Free University of Brussels, Brussels, Belgium

  Bob Coecke

• Department of Theoretical Physics, University of Geneva, Geneva, Switzerland

  David Moore

• Department of Mathematics and Computer Science, Juniata College, Huntingdon, USA

  Alexander Wilce

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