Mathematical Logic - Wei Li

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Résumé :
Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and G?del?s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students inrelevant disciplines.

Biographie:
Wei Li is Professor at the School of Computer Science and Engineering and Director of the National Laboratory of Software Development Environment?at Beihang University in Beijing, China.

Sommaire:
Dr Tan is a member of the academic staff at the Nanyang Technological University, Singapore, and has been working on interconnect reliability for more than 10 years. He has published more than 150 technical papers in this area. His work includes the numerical modeling of interconnect reliability, reliability physics of interconnects, testing methodologies of interconnect reliability, failure analysis of interconnects, and statistical analysis of interconnect reliability data. He has trained several research staff in this area, including research fellows, research associates, PhD students and industrial engineers. He has had published a 173-page review article on electromigration in the Material Science and Engineering Review, and is the sole author of the book Electromigration in ULSI Interconnection, published by World Scientific. He is currently IEEE Distinguished Lecturer in the area of reliability, Fellow of Singapore Quality Institute, and Senior Member of ASQ and IEEE. Dr. Li received his B.Eng and PhD from the School of Electrical and Electronic Engineering at Nanyang Technological University (NTU), Singapore, in 2005 and 2009 respectively. He was Process Integration Engineer in Systems on Silicon Manufacturing Co Pte Ltd (SSMC) from 2007 to 2009. He is one of the five recipients of the global inaugural prestige 2007 IEEE Electronic Device Society Master's Student Fellowship. In 2009, he joined the Singapore Institute of Manufacturing Technology (SIMTech), one of the research institutes in the Agency of Science, Technology and Research (A*STAR), as research scientist. His research interests include IC interconnection reliability and modeling, semiconductor device physics and reliability. Dr Gan has extensive hands-on experience, beginning in 2001, in the application of the finite element method to reliability analysis. He has over 10 years of diverse technical and management experience in research and development of semiconductor reliability solutions and ideas on manufacturing. From 2001 to 2006, he was a research fellow with the School of Electrical and Electronic Engineering and School of Materials Science and Engineering, Nanyang Technological University, Singapore. In 2006, he joined Semiconductor Manufacturing International Corporation (SMIC), Shanghai, China, as a principal engineer in the Logic Technology Development Center. He is currently a reliability senior manager in the Technology R&D Center, managing a team responsible for process reliability improvement and evaluation (both FEOL and BEOL) for advanced technology nodes. Dr Gan has had more than 50 technical papers on finite element methods, ULSI interconnect reliability, and semiconductor reliability, published in refereed journals and international conferences, and 10 patents filed in China. Dr Hou received his B.Eng and PhD from the School of Electrical and Electronic Engineering at Nanyang Technological University (NTU), Singapore, in 2005 and 2010 respectively. He has been working as a process integration engineer in Systems on Silicon Manufacturing Co Pte Ltd (SSMC) since 2009. His research interests are electromigration and stress induced voiding in IC interconnections....