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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.
"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.
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