Search Results for: the-computer-modelling-of-mathematical-reasoning

Author: Wang Pei

Publisher: World Scientific

ISBN: 9814440299

Category: Computers

Page: 276

View: 3890

This book provides a systematic and comprehensive description of Non-Axiomatic Logic, which is the result of the author's research for about three decades.Non-Axiomatic Logic is designed to provide a uniform logical foundation for Artificial Intelligence, as well as an abstract description of the “laws of thought” followed by the human mind. Different from “mathematical” logic, where the focus is the regularity required when demonstrating mathematical conclusions, Non-Axiomatic Logic is an attempt to return to the original aim of logic, that is, to formulate the regularity in actual human thinking. To achieve this goal, the logic is designed under the assumption that the system has insufficient knowledge and resources with respect to the problems to be solved, so that the “logical conclusions” are only valid with respect to the available knowledge and resources. Reasoning processes according to this logic covers cognitive functions like learning, planning, decision making, problem solving, etc.This book is written for researchers and students in Artificial Intelligence and Cognitive Science, and can be used as a textbook for courses at graduate level, or upper-level undergraduate, on Non-Axiomatic Logic.

Modelling and Reasoning about Systems

Author: Michael Huth,Mark Ryan

Publisher: Cambridge University Press

ISBN: 113945305X

Category: Computers

Page: N.A

View: 380

Recent years have seen the development of powerful tools for verifying hardware and software systems, as companies worldwide realise the need for improved means of validating their products. There is increasing demand for training in basic methods in formal reasoning so that students can gain proficiency in logic-based verification methods. The second edition of this successful textbook addresses both those requirements, by continuing to provide a clear introduction to formal reasoning which is both relevant to the needs of modern computer science and rigorous enough for practical application. Improvements to the first edition have been made throughout, with extra and expanded sections on SAT solvers, existential/universal second-order logic, micro-models, programming by contract and total correctness. The coverage of model-checking has been substantially updated. Further exercises have been added. Internet support for the book includes worked solutions for all exercises for teachers, and model solutions to some exercises for students.

Author: Mordechai Ben-Ari

Publisher: Springer Science & Business Media

ISBN: 1447141296

Category: Mathematics

Page: 346

View: 1089

Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableaux-based techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems. The logical systems presented are: propositional logic, first-order logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logic for the verification of concurrent programs. The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking.

A Resource for Teaching Mathematics

Author: Amy Shell-Gellasch

Publisher: MAA

ISBN: 0883851822

Category: Education

Page: 177

View: 1448

Research shows that students learn best when they actively participate in their learning. In particular, hands-on activities provide the greatest opportunities for gaining understanding and promoting retention. Apart from simple manipulatives, the mathematics classroom offers few options for hands-on activities. However, the history of mathematics offers many ways to incorporate hands-on learning. By bringing this material culture of mathematics into the classroom, students can experience historical applications and uses of mathematics in a setting rich in discovery and intellectual interest. This volume is a compilation of articles from researchers and educators who use the history of mathematics to facilitate active learning in the classroom. The contributions range from simple devices, such as the rectangular protractor, to elaborate models of descriptive geometry. Other chapters provide detailed descriptions on how to build and use historical models in the high school or collegiate classroom.

Author: Chris Sangwin

Publisher: OUP Oxford

ISBN: 0191635863

Category: Mathematics

Page: 200

View: 8215

Assessment is a key driver in mathematics education. This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded and, in articulating precisely the desired criteria, the teacher needs to think very carefully about the goals of the task. Hence CAA acts as a vehicle to examine assessment and mathematics education in detail and from a fresh perspective. One example is how it is natural for busy teachers to set only those questions that can be marked by hand in a straightforward way, even though the constraints of paper-based formats restrict what they do and why. There are other kinds of questions, such as those with non-unique correct answers, or where assessing the properties requires the marker themselves to undertake a significant computation. It is simply not sensible for a person to set these to large groups of students when marking by hand. However, such questions have their place and value in provoking thought and learning. This book, aimed at teachers in both schools and universities, explores how, in certain cases, different question types can be automatically assessed. Case studies of existing systems have been included to illustrate this in a concrete and practical way.

Author: Michael Jee

Publisher: John Wiley & Sons

ISBN: 1405152990

Category: Technology & Engineering

Page: 224

View: 5821

Quality assessment and the need for authentication are important features of the food and personal care products industries. This volume provides an overview of the methods relevant to analysis and authentication of oils and fats. All the major oils and fats are included. Chapter authors are drawn from the academic and industrial sectors. The volume is directed at chemists and technologists working in the food industry, the pharmaceutical industry and in oils and fats processing. It will also be of interest to analytical chemists and quality assurance personnel.

Mathematical Modeling in Context

Author: Greg Langkamp,Joseph Hull

Publisher: Pearson College Division

ISBN: 9780131485273

Category: Mathematics

Page: 354

View: 1589

An introductory quantitative math book with an environmental theme. The emphasis of this text is on analyzing real environmental information and problems, using mathematics accessible to students with an intermediate algebra background. Students using this text will develop mathematical (and environmental) literacy as they model natural processes using algebraic, graphical and numerical methods, and analyze data quantitatively to assist in objective decision making. The textbook is comprised of 4 principal sections: (1) basic numeracy; (2) function modeling; (3) difference equation modeling, and; (4) elementary statistics. Furthermore, this textbook combines both a reform and traditional approach. Traditional in that each chapter presents introductory material, worked examples, multiple student problems, and solutions to odd exercises. It is reform in that it investigates material through a synthesis of algebraic, graphical, numerical and verbal approaches.

Essays in Honor of Jörg H. Siekmann on the Occasion of His 60th Birthday

Author: Dieter Hutter,Werner Stephan

Publisher: Springer

ISBN: 354032254X

Category: Computers

Page: 570

View: 3713

By presenting state-of-the-art results in logical reasoning and formal methods in the context of artificial intelligence and AI applications, this book commemorates the 60th birthday of Jörg H. Siekmann. The 30 revised reviewed papers are written by former and current students and colleagues of Jörg Siekmann; also included is an appraisal of the scientific career of Jörg Siekmann entitled "A Portrait of a Scientist: Logics, AI, and Politics." The papers are organized in four parts on logic and deduction, applications of logic, formal methods and security, and agents and planning.

Author: Edward A. Bender

Publisher: Courier Corporation

ISBN: 0486137120

Category: Mathematics

Page: 272

View: 8431

Accessible text features over 100 reality-based examples pulled from the science, engineering, and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

Proceedings of CAD86, the Seventh International Conference on the Computer as a Design Tool, London, 2 - 5 September 1986, Organized by the Journal Computer-Aided Design

Author: Alison Smith

Publisher: Butterworth-Heinemann

ISBN: N.A

Category: Architecture

Page: 476

View: 497

Author: Judea Pearl

Publisher: Cambridge University Press

ISBN: 1139643983

Category: Science

Page: N.A

View: 846

Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. Cited in more than 2,100 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interest to students and professionals in a wide variety of fields. Dr Judea Pearl has received the 2011 Rumelhart Prize for his leading research in Artificial Intelligence (AI) and systems from The Cognitive Science Society.

Author: L. Magnani,Nancy J. Nersessian,Claudio Pizzi

Publisher: Springer Science & Business Media

ISBN: 9781402007125

Category: Computers

Page: 339

View: 5412

The study of diagnostic, visual, spatial, analogical, and temporal reasoning has demonstrated that there are many ways of performing intelligent and creative reasoning that cannot be described with the help only of traditional notions of reasoning such as classical logic. Understanding the contribution of modeling practices to discovery and conceptual change in science requires expanding scientific reasoning to include complex forms of creative reasoning that are not always successful and can lead to incorrect solutions. The study of these heuristic ways of reasoning is situated at the crossroads of philosophy, artificial intelligence, cognitive psychology, and logic; that is, at the heart of cognitive science. There are several key ingredients common to the various forms of model-based reasoning. The term 'model' comprises both internal and external representations. The models are intended as interpretations of target physical systems, processes, phenomena, or situations. The models are retrieved or constructed on the basis of potentially satisfying salient constraints of the target domain. Moreover, in the modeling process, various forms of abstraction are used. Evaluation and adaptation take place in light of structural, causal, and/or functional constraints. Model simulation can be used to produce new states and enable evaluation of behaviors and other factors.

Author: Kees Doets,Jan van Eijck,Jan Eijck

Publisher: Kings College Publications

ISBN: N.A

Category: Mathematics

Page: 426

View: 4641

Long ago, when Alexander the Great asked the mathematician Menaechmus for a crash course in geometry, he got the famous reply There is no royal road to mathematics. Where there was no shortcut for Alexander, there is no shortcut for us. Still, the fact that we have access to computers and mature programming languages means that there are avenues for us that were denied to the kings and emperors of yore. The purpose of this book is to teach logic and mathematical reasoning in practice, and to connect logical reasoning with computer programming in Haskell. Haskell emerged in the 1990s as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvelous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures. This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book, the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others. This is the updated, expanded, and corrected second edition of a much-acclaimed textbook. Praise for the first edition: Doets and van Eijck s The Haskell Road to Logic, Maths and Programming is an astonishingly extensive and accessible textbook on logic, maths, and Haskell. Ralf Laemmel, Professor of Computer Science, University of Koblenz-Landau

Research in Contexts of Practice : [proceedings of the NATO Advanced Research Workshop on Advances in Mathematical Problem Solving Research, Held in Viana Do Castelo, Portugal, 27-30 April, 1991]

Author: Joao P. Ponte

Publisher: Springer Science & Business Media

ISBN: 9783540557357

Category: Computers

Page: 346

View: 4281

This NATO volume discusses the implications of new information technologies and cognitive psychology for mathematical problem solving research and practice. It includes a discussion of problem solving and provides a view of developments in computerized learning environments.

Author: D. Corfield,Jon Williamson

Publisher: Springer Science & Business Media

ISBN: 9781402002236

Category: Business & Economics

Page: 413

View: 4403

Foundations of Bayesianism is an authoritative collection of papers addressing the key challenges that face the Bayesian interpretation of probability today. Some of these papers seek to clarify the relationships between Bayesian, causal and logical reasoning. Others consider the application of Bayesianism to artificial intelligence, decision theory, statistics and the philosophy of science and mathematics. The volume includes important criticisms of Bayesian reasoning and also gives an insight into some of the points of disagreement amongst advocates of the Bayesian approach. The upshot is a plethora of new problems and directions for Bayesians to pursue. The book will be of interest to graduate students or researchers who wish to learn more about Bayesianism than can be provided by introductory textbooks to the subject. Those involved with the applications of Bayesian reasoning will find essential discussion on the validity of Bayesianism and its limits, while philosophers and others interested in pure reasoning will find new ideas on normativity and the logic of belief.

abstracts and index to research on AI theory and applications, 1954-1987

Author: N.A

Publisher: Scientific Datalink

ISBN: N.A

Category: Computers

Page: 5

View: 5901

Author: Cheryl Hurkett,Laurence Rogers

Publisher: Lulu.com

ISBN: 1446162192

Category:

Page: 358

View: 9994

Proceedings of the Fourth Asian Symposium (ASCM 2000)

Author: Xiao-Shan Gao,Dongming Wang

Publisher: World Scientific

ISBN: 9810244983

Category: Computers

Page: 324

View: 9474

This volume contains selected papers presented at the Fourth Asian Symposium on Computer Mathematics. 39 peer-reviewed original contributions together with full papers and extended abstracts by the four invited speakers, G H Gonnet, D Lazard, W McCune, and W-T Wu, cover some of the most recent and significant advances in computer mathematics, including algebraic, symbolic, numeric, and geometric computation, automated mathematical reasoning, mathematical software, and computer-aided geometric design. Researchers, teachers, students, and engineers interested in doing mathematics using computers will find this volume good reading and a valuable reference.

Author: John O'Donnell,Cordelia Hall,Rex Page

Publisher: Springer Science & Business Media

ISBN: 1846285984

Category: Computers

Page: 441

View: 2732

Computer science abounds with applications of discrete mathematics, yet s- dents of computer science often study discrete mathematics in the context of purely mathematical applications. They have to ?gure out for themselves how to apply the ideas of discrete mathematics to computing problems. It is not easy. Most students fail to experience broad success in this enterprise, which is not surprising, since many of the most important advances in science and engineeringhavebeen, precisely, applicationsofmathematicstospeci?cscience and engineering problems. Tobesure,mostdiscretemathtextbooksincorporatesomeaspectsapplying discrete math to computing, but it usually takes the form of asking students to write programs to compute the number of three-ball combinations there are in a set of ten balls or, at best, to implement a graph algorithm. Few texts ask students to use mathematical logic to analyze properties of digital circuits or computer programs or to apply the set theoretic model of functions to understand higher-order operations. A major aim of this text is to integrate, tightly, the study of discrete mathematics with the study of central problems of computer science.