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The Classical Decision Problem by Egon Börger,Erich Grädel,Yuri Gurevich Pdf
This book offers a comprehensive treatment of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. The text presents a revealing analysis of the natural order of decidable and undecidable cases and includes a number of simple proofs and exercises.
The Classical Decision Problem by Egon Börger,Erich Grädel,Yuri Gurevich Pdf
This book offers a comprehensive treatment of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. The text presents a revealing analysis of the natural order of decidable and undecidable cases and includes a number of simple proofs and exercises.
Recursive Functions and Metamathematics by Roman Murawski Pdf
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.
The Emergent Multiverse presents a striking new account of the 'many worlds' approach to quantum theory. The point of science, it is generally accepted, is to tell us how the world works and what it is like. But quantum theory seems to fail to do this: taken literally as a theory of the world, it seems to make crazy claims: particles are in two places at once; cats are alive and dead at the same time. So physicists and philosophers have often been led either to give up on the idea that quantum theory describes reality, or to modify or augment the theory. The Everett interpretation of quantum mechanics takes the apparent craziness seriously, and asks, 'what would it be like if particles really were in two places at once, if cats really were alive and dead at the same time'? The answer, it turns out, is that if the world were like that—if it were as quantum theory claims—it would be a world that, at the macroscopic level, was constantly branching into copies—hence the more sensationalist name for the Everett interpretation, the 'many worlds theory'. But really, the interpretation is not sensationalist at all: it simply takes quantum theory seriously, literally, as a description of the world. Once dismissed as absurd, it is now accepted by many physicists as the best way to make coherent sense of quantum theory. David Wallace offers a clear and up-to-date survey of work on the Everett interpretation in physics and in philosophy of science, and at the same time provides a self-contained and thoroughly modern account of it—an account which is accessible to readers who have previously studied quantum theory at undergraduate level, and which will shape the future direction of research by leading experts in the field.
Epistemic Foundations of Fuzziness by Kofi Kissi Dompere Pdf
It is necessary to practice methodological doubt, like Descartes, in - der to loosen the hold of mental habits; and it is necessary to cultivate logical imagination, in order to have a number of hypotheses at c- mand, and not to be the slave of the one which common sense has r- dered easy to imagine. These two processes, of doubting the familiar and imagining the unfamiliar, are corrective, and form the chief part of the mental training required for a philosopher. Bertrand Russell At every stage and in all circumstances knowledge is incomplete and provisional, conditioned and limited by the historical circumstances under which it was acquired, including the means and methods used for gaining it and the historically conditioned assumptions and categories used in the formulation of ideas and conclusions. Maurice Cornforth This monograph is the second in the series of meta-theoretic analysis of fuzzy paradigm and its contribution and possible contribution to formal reasoning in order to free the knowledge production process from the ridge frame of the classical paradigm that makes its application to soft and inexact sciences d- ficult or irrelevant. The work in the previous monograph was strictly devoted to problems of theory of knowledge and critique of classical, bounded and other rationalities in decision-choice processes regarding the principles of verification, falsification or corroboration in knowledge production. This monograph deals mostly with epistemic decision-choice models and theories and how they are related to both the classical and fuzzy paradigms.
Introduction to Statistical Decision Theory by Silvia Bacci,Bruno Chiandotto Pdf
Introduction to Statistical Decision Theory: Utility Theory and Causal Analysis provides the theoretical background to approach decision theory from a statistical perspective. It covers both traditional approaches, in terms of value theory and expected utility theory, and recent developments, in terms of causal inference. The book is specifically designed to appeal to students and researchers that intend to acquire a knowledge of statistical science based on decision theory. Features Covers approaches for making decisions under certainty, risk, and uncertainty Illustrates expected utility theory and its extensions Describes approaches to elicit the utility function Reviews classical and Bayesian approaches to statistical inference based on decision theory Discusses the role of causal analysis in statistical decision theory
Foundations of Information Technology in the Era of Network and Mobile Computing by Ricardo Baeza-Yates,Ugo Montanari,Nicola Santoro Pdf
Foundations of Information Technology in the Era of Network and Mobile Computing is presented in two distinct but interrelated tracks: -Algorithms, Complexity and Models of Computation; -Logic, Semantics, Specification and Verification. This volume contains 45 original and significant contributions addressing these foundational questions, as well as 4 papers by outstanding invited speakers. These papers were presented at the 2nd IFIP International Conference on Theoretical Computer Science (TCS 2002), which was held in conjunction with the 17th World Computer Congress, sponsored by the International Federation for Information Processing (IFIP), and which convened in Montréal, Québec, Canada in August 2002.
Fuzzy Preference Ordering of Interval Numbers in Decision Problems by Atanu Sengupta,Tapan Kumar Pal Pdf
In conventional mathematical programming, coefficients of problems are usually determined by the experts as crisp values in terms of classical mathematical reasoning. But in reality, in an imprecise and uncertain environment, it will be utmost unrealistic to assume that the knowledge and representation of an expert can come in a precise way. The wider objective of the book is to study different real decision situations where problems are defined in inexact environment. Inexactness are mainly generated in two ways – (1) due to imprecise perception and knowledge of the human expert followed by vague representation of knowledge as a DM; (2) due to huge-ness and complexity of relations and data structure in the definition of the problem situation. We use interval numbers to specify inexact or imprecise or uncertain data. Consequently, the study of a decision problem requires answering the following initial questions: How should we compare and define preference ordering between two intervals?, interpret and deal inequality relations involving interval coefficients?, interpret and make way towards the goal of the decision problem? The present research work consists of two closely related fields: approaches towards defining a generalized preference ordering scheme for interval attributes and approaches to deal with some issues having application potential in many areas of decision making.
This book constitutes the refereed proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science, STACS 97, held in Lübeck, Germany, in February/March 1997. The 46 revised full papers included were carefully selected from a total of 139 submissions; also included are three invited full papers. The papers presented span the whole scope of theoretical computer science. Among the topics covered are, in particular, algorithms and data structures, computational complexity, automata and formal languages, structural complexity, parallel and distributed systems, parallel algorithms, semantics, specification and verification, logic, computational geometry, cryptography, learning and inductive inference.
Cost-Benefit Analysis and the Theory of Fuzzy Decisions by K. K. Dompere Pdf
This monograph is devoted to the identification and measurement theory of costs and benefits in a fuzzy information environment. The process of cost-benefit analysis is presented, requiring the development of real cost-benefit databases and the construction of cost-benefit criterion. These steps are accomplished with various theoretical constructs that provide sets of self-contained algorithms for application. This book integrates cost-benefit analysis, theory of fuzzy decisions and social decisions into unified decision algorithms accessible to practitioners, researchers, and graduate students. It features the essentials of fuzzy mathematics and algorithms in a comprehensive way, exposing a multi-disciplinary approach for the development of cost-benefit decision making in the framework of fuzziness and soft computing.
Comparative Decision Making by Philip H. Crowley,Thomas R. Zentall Pdf
Decision making cuts across most areas of intellectual enquiry and academic endeavor. The classical view of individual human thinkers choosing among options remains important and instructive, but the contributors to this volume broaden this perspective to characterize the decision making behavior of groups, non-human organisms and even non-living objects and mathematical constructs. A diverse array of methods is brought to bear-mathematical, computational, subjective, neurobiological, evolutionary, and cultural. We can often identify best or optimal decisions and decision making processes, but observed responses may deviate markedly from these, to a large extent because the environment in which decisions must be made is constantly changing. Moreover, decision making can be highly constrained by institutions, natural and social context, and capabilities. Studies of the mechanisms underlying decisions by humans and other organisms are just beginning to gain traction and shape our thinking. Though decision making has fundamental similarities across the diverse array of entities considered to be making them, there are large differences of degree (if not kind) that relate to the question of human uniqueness. From this survey of views and approaches, we converge on a tentative agenda for accelerating development of a new field that includes advancing the dialog between the sciences and the humanities, developing a defensible classification scheme for decision making and decision makers, addressing the role of morality and justice, and moving advances into applications-the rapidly developing field of decision support.
The aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D. An important strength of this book is that it provides a mathematically rigorous and even-handed account of both Classical and Bayesian inference in order to give readers a broad perspective. For example, the "uniformly most powerful" approach to testing is contrasted with available decision-theoretic approaches.
Fields of Logic and Computation by Andreas Blass,Nachum Dershowitz,Wolfgang Reisig Pdf
Yuri Gurevich has played a major role in the discovery and development of - plications of mathematical logic to theoretical and practical computer science. His interests have spanned a broad spectrum of subjects, including decision p- cedures, the monadic theory of order, abstract state machines, formal methods, foundations of computer science, security, and much more. In May 2010, Yuri celebrated his 70th birthday. To mark that occasion, on August 22, 2010,a symposium was held in Brno, the Czech Republic, as a sat- lite event of the 35th International Symposium on Mathematical Foundations of Computer Science (MFCS 2010) and of the 19th EACSL Annual Conference on Computer Science Logic (CSL 2010). The meeting received generous support from Microsoft Research. In preparation for this 70th birthday event, we asked Yuri’s colleagues (whether or not they were able to attend the symposium) to contribute to a volume in his honor. This book is the result of that e?ort. The collection of articles herein begins with an academic biography, an annotated list of Yuri’s publications and reports, and a personaltribute by Jan Van den Bussche. These are followed by 28 technical contributions. These articles – though they cover a broad range of topics – represent only a fraction of Yuri’s multiple areas of interest. Each contribution was reviewed by one or two readers. In this regard, the editors wish to thank several anonymous individuals for their assistance.
