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(全新特價) 書名：The Mathematics of Logic: A Guide to Completeness Theorems and Their Applications 作者：KAYE 出版社：Cambridge 出版日期：2007/00/00 ISBN：9780521708777
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The Mathematics of Logic 2007 <CAM> 978-0-521-70877-7
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詳細資訊
(全新特價) 書名：The Mathematics of Logic: A Guide to Completeness Theorems and Their Applications 作者：KAYE 出版社：Cambridge 出版日期：2007/00/00 ISBN：9780521708777
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Epistemic logic has grown from its philosophical beginnings to find diverse applications in computer science as a means of reasoning about the knowledge and belief of agents. This book, based on courses taught at universities and summer schools, provides a broad introduction to the subject; many exercises are included together with their solutions. The authors begin by presenting the necessary apparatus from mathematics and logic, including Kripke semantics and the well-known modal logics K, T, S4 and S5. Then they turn to applications in the contexts of distributed systems and artificial intelligence: topics that are addressed include the notions of common knowledge, distributed knowledge, explicit and implicit belief, the interplays between knowledge and time, and knowledge and action, as well as a graded (or numerical) variant of the epistemic operators. The problem of logical omniscience is also discussed extensively. Halpern and Moses' theory of honest formulae is covered, and a digression is made into the realm of non-monotonic reasoning and preferential entailment. Moore's autoepistemic logic is discussed, together with Levesque's related logic of 'all I know'. Furthermore, it is shown how one can base default and counterfactual reasoning on epistemic logic.
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書名：Discrete Mathematics and Its Applications 8/E 作者：Rosen 出版社：McGraw-Hill 出版日期：2018/08/00 ISBN：9781260091991
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This book presents new developments in the open quantum systems theory with emphasis on applications to the (frequent) measurement theory. In the first part of the book, the uniqueness theorems for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions are discussed. The major theme involves an intrinsic characterization of the simplest symmetric operator solutions to the Heisenberg uncertainty relations, the problem posed by Jørgensen and Muhly, followed by the proof of the uniqueness theorems for the simplest solutions to the restricted Weyl commutation relations. The detailed study of unitary invariants of the corresponding dissipative and symmetric operators opens up a look at the classical Stone-von Neumann uniqueness theorem from a new angle and provides an extended version of the uniqueness result relating various realizations of a differentiation operator on the corresponding metric graphs. The second part of the book is devoted to mathematical problems of the quantum measurements under continuous monitoring. Among the topics discussed are the complementarity of the Quantum Zeno effect and Exponential Decay scenario in frequent quantum measurements, and a rigorous treatment, within continuous monitoring paradigm, of the celebrated "double-slit experiment" where the renowned exclusive and interference measurement alternatives approach in quantum theory is presented in a way that is accessible for mathematicians. One of the striking applications of the generalized (1-stable) central limit theorem is the mathematical evidence of exponential decay of unstable states of the quantum pendulum under continuous monitoring. Sample Chapter(s) Preface Chapter 1: INTRODUCTION Contents: Acknowledgments Preface Representations of Operator Commutation Relations: Introduction Preliminaries and Basic Definitions The Commutation Relations and Character-Automorphic Functions The Differentiation Operator on Metric Graphs The Magnetic Hamiltonian The Livšic Function s(Ḋ,DΘ)(z) The Weyl-Titchmarsh Function M(Ḋ,DΘ)(z) The Model Dissipative Operators The Characteristic Function S(Ḋ,Ḓ,DΘ)(z) The Transmission Coefficient and the Characteristic Function Uniqueness Results Dissipative Solutions to the CCR Main Results Unitary Dynamics on the Full Graph Continuous Monitoring, Quantum Measurements: Continuous Monitoring of the Quantum Systems The Quantum Zeno versus Anti-zeno Effect Alternative The Quantum Zeno Effect versus Exponential Decay Alternative Preliminaries: Probabilities versus Amplitudes Massless Particles on a Ring Continuous Monitoring with Interference Continuous Monitoring with No Interference The Self-adjoint Dilation General Open Quantum Systems on a Ring Operator Coupling Limit Theorems Appendices: The Characteristic Function for Rank-One Perturbations Prime Symmetric Operators A Functional Model of a Triple The Spectral Analysis of the Model Dissipative Operator Transformation Laws The Invariance Principle The Operator Coupling and the Multiplication Theorem Stable Laws References Index Readership: Graduates and Researchers interested in mathematical physics, operator theory, quantum physics.
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