What link might connect two far worlds like quantum theory and music? There is something universal in the mathematical formalism of quantum theory that goes beyond the limits of its traditional physical applications. We are now beginning to understand how some mysterious quantum concepts, like superposition and entanglement, can be used as a semantic resource.

This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main "mathematical characters" of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein-Podolsky-Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like "Alice knows that everybody knows that she is pretty", explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.

"Is quantum logic really logic?" This book argues for a positive answer to this question once and for all. There are many quantum logics and their structures are delightfully varied. The most radical aspect of quantum reasoning is reflected in unsharp quantum logics, a special heterodox branch of fuzzy thinking.
For the first time, the whole story of Quantum Logic is told; from its beginnings to the most recent logical investigations of various types of quantum phenomena, including quantum computation. Reasoning in Quantum Theory is designed for logicians, yet amenable to advanced graduate students and researchers of other disciplines.

A vivid and comprehensive picture of the current state of research in all directions of logic and philosophy of science. The book presents a wide combination of papers containing relevant technical results in the foundations of science and papers devoted to conceptual analyses, deeply rooted in advanced present-day research. Audience: The volume is attractive both for specialists in foundational questions and scholars interested in general epistemology.

This book provides an interdisciplinary approach to one of the most fascinating and important open questions in science: What is quantum mechanics really talking about? In the last decades quantum mechanics has given rise to a new quantum technological era, a revolution taking place today especially within the field of quantum information processing; which goes from quantum teleportation and cryptography to quantum computation. Quantum theory is probably our best confirmed physical theory. However, in spite of its great empirical effectiveness it stands today still without a universally accepted physical representation that allows us to understand its relation to the world and reality.The novelty of the book comes from the multiple perspectives put forward by top researchers in quantum mechanics, from Europe as well as North and South America, discussing the meaning and structure of the theory of quanta. The book comprises in a balanced manner physical, philosophical, logical and mathematical approaches to quantum mechanics and quantum information. Going from quantum superpositions and entanglement to dynamics and the problem of identity; from quantum logic, computation and quasi-set theory to the category approach and teleportation; from realism and empiricism to operationalism and instrumentalism; the book considers from different angles some of the most intriguing questions in the field.From Buenos Aires to Brussels and Cagliari, from Florence to Florianopolis, the interaction between different groups is reflected in the many different articles. This book is interesting not only to the specialists but also to the general public attempting to get a grasp on some of the most fundamental questions of present quantum physics.

"Is quantum logic really logic?" This book argues for a positive answer to this question once and for all. There are many quantum logics and their structures are delightfully varied. The most radical aspect of quantum reasoning is reflected in unsharp quantum logics, a special heterodox branch of fuzzy thinking.
For the first time, the whole story of Quantum Logic is told; from its beginnings to the most recent logical investigations of various types of quantum phenomena, including quantum computation. Reasoning in Quantum Theory is designed for logicians, yet amenable to advanced graduate students and researchers of other disciplines.

A vivid and comprehensive picture of the current state of research in all directions of logic and philosophy of science. The book presents a wide combination of papers containing relevant technical results in the foundations of science and papers devoted to conceptual analyses, deeply rooted in advanced present-day research. Audience: The volume is attractive both for specialists in foundational questions and scholars interested in general epistemology.