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 philosophy, 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.

Includes bibliographical references (pages 405-409) and index.

Cover -- CONTENTS -- PREFACE -- CONTENTS -- INTRODUCTION -- Conception of the book -- The history of the subject -- State of the art -- CHAPTER 0. PROBLEM CLASSIFICATION. INTRODUCTION TO THE SOLVING METHODS -- 0.1 What is a problem? -- 0.2 Problem classification -- 0.3 An approach to building an interpretation calculus -- 0.4 Finding a solution by means of theorem proving -- 0.5 Finding an optimum interpretation -- 0.6 Psychological aspects -- 0.7 Conclusion -- CHAPTER 1. ELEMENTS OF PROBLEM SOLVING THEORY: APPLICATION OF CUTTING STRATEGIES -- 1.1 Introduction -- 1.2 The properties of a solution's elements -- 1.3 A system of axioms for incompatibility calculus -- 1.4 An algorithm for searching for maximum-size zero submatrix -- 1.5 On the minimum-size cover problem (MSCP) -- 1.6 Precedence and incompatibility -- 1.7 Prohibition -- 1.8 Conditional executability -- 1.9 Other examples -- 1.10 Conclusion -- CHAPTER 2. SOLVING DISCRETE OPTIMIZATION PROBLEMS ON THE BASIS OF?-TRANSFORM METHOD -- 2.1?-transform method -- 2.2 Some important cases of the analytical representation of the?(q)-function -- 2.3 A general scheme for the discrete? -transform method -- 2.4 An approximate solution to F-indefinite static optimization problems -- 2.5 Conclusion -- CHAPTER 3. WEAK METHODS AND HEURISTIC REASONING -- 3.1 Specific features of solving tasks by weak methods -- 3.2 Control of the solving process -- 3.3 Models of heuristic-based solution searching -- 3.4 Try-and-test procedures with cutting -- 3.5 Intermediate remarks on heuristics utilization -- 3.6 Examples of problem solving principles -- 3.7 Solution tree -- 3.8 Principle of dominance and choice function -- 3.9 An example of mechanization of heuristics -- 3.10 Conclusion -- CHAPTER 4. LOGIC-BASED PROBLEM SOLVERS: APPROACHES AND NEW METHODS -- 4.1 Introduction -- 4.2 Logical problem solvers -- 4.3 Group resolution principle in predicate calculus -- 4.4 Implementation of group resolution principle -- 4.5 Reduction algorithm with term re-writing -- 4.6 Conclusion -- CHAPTER 5. PROGRAMMING CONCEPTS IN PROBLEM SOLVING -- 5.1. Programming or theorem proving? -- 5.2 Universal algorithm paradigm -- 5.3 Computer mathematics -- 5.4 Expert systems -- 5.5 Evolutionary problem solution synthesis (EPSS) concept -- 5.6 Mathematical induction and pattern recognition approaches -- 5.7 Intellectual support concept in the problem solving system -- 5.8 Making a semantic structure of the problem -- 5.9 Conclusion -- CHAPTER 6. FUTURE CONCEPTS: SOME PHILOSOPHICAL ISSUES -- 6.1 Universal problem solving approach restoration -- 6.2 Weak methods become strong -- 6.3 The role of formal logic in future developments -- 6.4 The human factor -- 6.5 Are there other paradigms? -- 6.6 Conclusive remarks -- REFERENCES -- GLOSSARY -- INDEX -- Last Page.

Print version record.

Elsevier ScienceDirect All Books