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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. 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 in relevant disciplines.

Mathematical logic --- Computer science --- informatiewetenschappen --- computers --- wiskunde --- logica --- computerkunde

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The objective of the book is to give a selection from the papers, which summarize several important results obtained within the framework of the József Hatvany Doctoral School operating at the University of Miskolc, Hungary. In accordance with the three main research areas of the Doctoral School established for Information Science, Engineering and Technology, the papers can be classified into three groups. They are as follows: (1) Applied Computational Science; (2) Production Information Engineering (IT for Manufacturing included); (3) Material Stream Systems and IT for Logistics. As regards the first area, some papers deal with special issues of algorithms theory and its applications, with computing algorithms for engineering tasks, as well as certain issues of data base systems and knowledge intensive systems. Related to the second research area, the focus is on Production Information Engineering with special regard to discrete production processes. In the second research area the papers show some new integrated systems suitable for optimizing discrete production processes in a top-down way. The papers connecting with the third research field deal with different issues of materials stream systems and logistics, taking into consideration of applied mathematical models and IT-tools. The book makes an effort to ensure certain equilibrium between theory and practice and to show some new approach both from theoretical modelling aspect, as well as experimental and practical point of view.  .

Operational research. Game theory --- Mathematical statistics --- Machine elements --- Applied physical engineering --- Planning (firm) --- Plant and equipment --- Production management --- Artificial intelligence. Robotics. Simulation. Graphics --- informatiewetenschappen --- neuronale netwerken --- fuzzy logic --- cybernetica --- mathematische modellen --- productie --- econometrie --- KI (kunstmatige intelligentie) --- operationeel onderzoek --- machines --- ingenieurswetenschappen --- AI (artificiële intelligentie)