Problem Solving: Methods, Programming and Future Concepts

Description

Problem solving is the very area of articifical intelligence AI which, probably, will never result in a complete set of formalized theories, in a pragmatic philosphy, or in a "universal" applied discipline. Studying questions concerning this area, encompasses different concepts, models and theories.

This volume of the series looks at classifying problems, interpreting them, and the methods of solving them. The final chapter covers future concepts such as universal problem solving approach restoration, weak methods becoming strong, the role of formal logic in future developments, human factors and other paradigms.

Different groups of readers such as mathematicians, specialists in computer sciences, and programmers will find this title of interest. Post-graduates and the students specializing in AI and applied mathematics will also find the work useful.

Front Cover 2
Problem Solving: Methods, Programming and Future Concepts 5
Copyright Page 6
PREFACE 7
CONTENTS 9
CONTENTS 9
INTRODUCTION 15
- Conception of the book 24
- The history of the subject 27
- State of the art 34
CHAPTER 0. PROBLEM CLASSIFICATION. INTRODUCTION TO THE SOLVING METHODS 47
- 0.1 What is a problem? 47
- 0.2 Problem classification 51
- 0.3 An approach to building an interpretation calculus 52
- 0.4 Finding a solution by means of theorem proving 75

Front Cover 2
Problem Solving: Methods, Programming and Future Concepts 5
Copyright Page 6
PREFACE 7
CONTENTS 9
CONTENTS 9
INTRODUCTION 15
- Conception of the book 24
- The history of the subject 27
- State of the art 34
CHAPTER 0. PROBLEM CLASSIFICATION. INTRODUCTION TO THE SOLVING METHODS 47
- 0.1 What is a problem? 47
- 0.2 Problem classification 51
- 0.3 An approach to building an interpretation calculus 52
- 0.4 Finding a solution by means of theorem proving 75
- 0.5 Finding an optimum interpretation 94
- 0.6 Psychological aspects 110
- 0.7 Conclusion 110
CHAPTER 1. ELEMENTS OF PROBLEM SOLVING THEORY: APPLICATION OF CUTTING STRATEGIES 111
- 1.1 Introduction 111
- 1.2 The properties of a solution's elements 113
- 1.3 A system of axioms for incompatibility calculus 115
- 1.4 An algorithm for searching for maximum-size zero submatrix 135
- 1.5 On the minimum-size cover problem (MSCP) 153
- 1.6 Precedence and incompatibility 159
- 1.7 Prohibition 161
- 1.8 Conditional executability 164
- 1.9 Other examples 168
- 1.10 Conclusion 170
CHAPTER 2. SOLVING DISCRETE OPTIMIZATION PROBLEMS ON THE BASIS OF ψ-TRANSFORM METHOD 171
- 2.1 ψ-transform method 172
- 2.2 Some important cases of the analytical representation of the ψ(q)-function 175
- 2.3 A general scheme for the discrete ψ -transform method 180
- 2.4 An approximate solution to F-indefinite static optimization problems 195
- 2.5 Conclusion 213
CHAPTER 3. WEAK METHODS AND HEURISTIC REASONING 215
- 3.1 Specific features of solving tasks by weak methods 215
- 3.2 Control of the solving process 218
- 3.3 Models of heuristic-based solution searching 224
- 3.4 Try-and-test procedures with cutting 227
- 3.5 Intermediate remarks on heuristics utilization 240
- 3.6 Examples of problem solving principles 241
- 3.7 Solution tree 246
- 3.8 Principle of dominance and choice function 280
- 3.9 An example of mechanization of heuristics 286
- 3.10 Conclusion 294
CHAPTER 4. LOGIC-BASED PROBLEM SOLVERS: APPROACHES AND NEW METHODS 297
- 4.1 Introduction 297
- 4.2 Logical problem solvers 298
- 4.3 Group resolution principle in predicate calculus 311
- 4.4 Implementation of group resolution principle 322
- 4.5 Reduction algorithm with term re-writing 328
- 4.6 Conclusion 338
CHAPTER 5. PROGRAMMING CONCEPTS IN PROBLEM SOLVING 339
- 5.1. Programming or theorem proving? 339
- 5.2 Universal algorithm paradigm 353
- 5.3 Computer mathematics 361
- 5.4 Expert systems 361
- 5.5 Evolutionary problem solution synthesis (EPSS) concept 370
- 5.6 Mathematical induction and pattern recognition approaches 372
- 5.7 Intellectual support concept in the problem solving system 374
- 5.8 Making a semantic structure of the problem 391
- 5.9 Conclusion 398
CHAPTER 6. FUTURE CONCEPTS: SOME PHILOSOPHICAL ISSUES 401
- 6.1 Universal problem solving approach restoration 401
- 6.2 Weak methods become strong 406
- 6.3 The role of formal logic in future developments 408
- 6.4 The human factor 411
- 6.5 Are there other paradigms? 415
- 6.6 Conclusive remarks 417
REFERENCES 419
GLOSSARY 425
INDEX 433

Author's affiliation

O.V. German: State University of Informatics and Radio Ele
D.V. Ofitserov: Catholic University of America, Washington, D

Methods, Programming and Future Concepts

Description

TOC

Reviews (0)

Author's affiliation