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

A Model of Intelligent Reasoning

Author: Pei Wang

Publisher: World Scientific

ISBN: 9814440280

Category: Computers

Page: 258

View: 7401

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 OC laws of thoughtOCO followed by the human mind. Different from OC mathematicalOCO 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 OC logical conclusionsOCO 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, 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: 3714

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: 2331

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.

Author: Chris Sangwin

Publisher: OUP Oxford

ISBN: 0191635863

Category: Mathematics

Page: 200

View: 7269

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: 3507

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.

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: 6410

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.

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: 9307

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.

Proceedings of the Fifth Asian Symposium (ASCM 2001), Matsuyama, Japan, 26-28 September 2001

Author: Kiyoshi Shirayanagi,Kazuhiro Yokoyama

Publisher: World Scientific

ISBN: 9789812799661

Category: Mathematics

Page: 240

View: 1868

This volume covers 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, engineers, academics and graduate students interested in doing mathematics using computers will find this volume good reading and a valuable reference. Contents: Solution of a Linear Differential Equations in the Form of Power Series and Its Application (T Kitamoto); On the Specification for Solvers of Polynomial Systems (D Lazard); OMEI: An Open Mathematical Engine Interface (W Liao et al.); Polynomial Solutions of Algebraic Differential Equations (Y Ma & X-S Gao); FIGUE: Mathematical Formula Layout with Interaction and MathML Support (H Naciri & L Rideau); An Inductive Approach to Formalizing Notions of Number Theory Proofs (T M Rasmussen); A Generalized Algorithm for Computing Characteristic Sets (D Wang); Action Refinement for Timed LOTOS (J Wu); Exact Analytical Solutions to a Set of Coupled Nonlinear Differential Equations Using Symbolic Computation (R-X Yao & Z-B Li); and other papers. Readership: Researchers, engineers, academics and graduate students in numerical & computational mathematics, theoretical computer science, mathematical modeling, analysis & differential equations, software engineering/programming, algebra & number theory, and logic.

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: 5147

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

Publisher: Springer Science & Business Media

ISBN: 9781402007125

Category: Computers

Page: 339

View: 1089

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: D. Corfield,Jon Williamson

Publisher: Springer Science & Business Media

ISBN: 9781402002236

Category: Business & Economics

Page: 413

View: 6680

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.

Authentic Problem Solving in Middle School

Author: Nancy Butler Wolf

Publisher: N.A

ISBN: 9780325062594

Category: Education

Page: 152

View: 4352

"Nancy's in-depth look at mathematical modeling offers middle school teachers the kind of practical help they need for incorporating modeling into their classrooms." -Cathy Seeley, Past President of NCTM, author of Faster Isn't Smarter and Smarter Than We Think "This is the book that math teachers and parents have been waiting for. Nancy provides a comprehensive step-by-step guide to modeling in mathematics at the middle school level." -David E. Drew, author of STEM the Tide: Reforming Science, Technology, Engineering, and Math Education in America We all use math to analyze everyday situations we encounter. Whether we realize it or not, we're modeling with mathematics: taking a complex situation and figuring out what we need to make sense of it. In Modeling with Mathematics, Nancy Butler Wolf shows that math is most powerful when it means something to students. She provides clear, friendly guidance for teachers to use authentic modeling projects in their classrooms and help their students develop key problem-solving skills, including: collecting data and formulating a mathematical model interpreting results and comparing them to reality learning to communicate their solutions in meaningful ways. This kind of teaching can be challenging because it is open-ended: it asks students to make decisions about their approach to a scenario, the information they will need, and the tools they will use. But Nancy proves there is ample middle ground between doing all of the work for your students and leaving them to flail in the dark. Through detailed examples and hands-on activities, Nancy shows how to guide your students to become active participants in mathematical explorations who are able to answer the question, "What did I just figure out?" Her approach values all students as important contributors and shows how instruction focused on mathematical modeling engages every learner regardless of their prior history of success or failure in math.

Author: Cheryl Hurkett,Laurence Rogers

Publisher: Lulu.com

ISBN: 1446162192

Category:

Page: 358

View: 9262

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 736

Author: Sheldon Scott Nicholl,University of Illinois at Urbana-Champaign. Department of Computer Science

Publisher: N.A

ISBN: N.A

Category: Language acquisition

Page: 264

View: 5688

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

Publisher: Springer Science & Business Media

ISBN: 1846285984

Category: Computers

Page: 441

View: 5598

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.

Author: Jeffrey Johnson,Sean McKee,Alfred Vella,Institute of Mathematics and Its Applications

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 328

View: 8561

This book offers a revelatory glimpse into the future--when science, social science, and social administration will be based on the complementary interplay between artificial intelligence, mathematics, and statistics. Comprised of contributions from a broad range of leading scientists and researchers, the book outlines how artificial intelligence supplies insights into the nature of complex problems, mathematics offers a rich language for presenting systems and methods for investigating them rigorously, and statistics provides the interface between theory and data from both observation and experiment. Students and researchers in applied mathematics, artificial intelligence, and statistics interested in the growing integration of computer technologies and modern mathematical breakthroughs will want to read this important new book.

Proceedings of the Fourth Asian Symposium (ASCM 2000)

Author: Xiao-Shan Gao,Dongming Wang

Publisher: World Scientific

ISBN: 9810244983

Category: Computers

Page: 324

View: 7869

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 Alan Robinson,Andreĭ Voronkov

Publisher: Gulf Professional Publishing

ISBN: 9780444829498

Category: Computers

Page: 2122

View: 3183

This first volume of the Handbook of Automated Reasoning includes topics such as: the early history of automated deduction, classical logic - resolution theorem proving, and tableaux and related methods.