Details
Mathematical Logic
Foundations for Information ScienceProgress in Computer Science and Applied Logic, Band 25
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64,19 € |
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| Verlag: | Birkhäuser |
| Format: | |
| Veröffentl.: | 26.02.2010 |
| ISBN/EAN: | 9783764399771 |
| Sprache: | englisch |
| Anzahl Seiten: | 273 |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
<P>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 Gödel’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. </P>
<P></P>
<P>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 in relevant disciplines.</P>
<P></P>
<P>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 in relevant disciplines.</P>
Syntax of First-Order Languages.- Models of First-Order Languages.- Formal Inference Systems.- Computability & Representability.- Gödel Theorems.- Sequences of Formal Theories.- Revision Calculus.- Version Sequences.- Inductive Inference.- Workflows for Scientific Discovery.
<P>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 Gödel’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. </P>
<P></P>
<P>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 in relevant disciplines.</P>
<P></P>
<P>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 in relevant disciplines.</P>
Research monograph of textbook style with well-structured presentation and formal proofs for all theoretical results, illustrated by concrete examples New ideas and methodologies from information science and technology are used to annotate the concepts and theorems of mathematical logic, providing a new angle of view for readers from mathematics and a friendly environment for readers from information science to understand the quintessence of mathematical logic The author’s original work on version sequences, revision calculus, and language environments is coherently integrated into the book, enriching the content and the scope of application of mathematical logic Includes supplementary material: sn.pub/extras
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