Special Issue: Quantum Information and Quantum Logic

Mauro D'Ariano, Andrei Yu. Khrennikov, Massimo Melucci

Johan van Benthem, Sonja Smets

This special issue is situated at the interface between Logic and the Foundations of Physics.This interface, though not as active as the logical foundations of mathematics, has long existed-with highlights such as "quantum logic", or studies of the general logical structure of physical theories.In recent years, more themes have come to the fore, and we may be witnessing a revival.The papers presented here emanate from a symposium held at the University of Utrecht in January 2008 with the aim of charting established as well as new connections between the two fields.One of the main questions discussed was whether and how modern techniques coming from logic, computer science and information theory might be combined with state-of-the-art insights in the philosophy of physics to gain a better understanding of the main foundational issues and open problems in modern physics.The success of this symposium has shown that there are several possible answers to this question.

Hai‐Zhi Song

Sonja Smets

Current research in Logic is no longer confined to the traditional study of logical consequence or valid inference. As can be witnessed by the range of topics covered in this special issue, the subject matter of logic encompasses several kinds of informational processes ranging from proofs and inferences to dialogues, observations, measurements, communication and computation. What interests us here is its application to quantum physics: how does logic handle informational processes such as observations and measurements of quantum systems? What are the basic logical principles fit to handle and reason about quantum physical processes? These are the central questions in this paper. It is my aim to provide the reader with some food for thought and to give some pointers to the literature that provide an easy access to this field of research. In the next section I give a brief historical sketch of the origin of the quantum logic project. Next I will explain the theory of orthomodular lat-tices in section 2. Section 3 covers the syntax and semantics of traditional

Jonas R. Becker Arenhart, Raoni Wohnrath Arroyo

We provide a brief introduction to the special issue dedicated to logical and metaphysical aspects of contemporary issues concerning identity and individuality in quantum mechanics. After a discussion of the main theme, we present the contributed papers and the historical motivations for the special issue.