Theoretical Approaches to Non-Numerical Problem Solving

1. Front Matter

   Pages N1-vi

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2. Overviews

   1. Front Matter

      Pages 1-1

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   2. An Overview of Mechanical Theorem Proving

      • J. A. Robinson

      Pages 2-20

   3. Game Playing Programs: An Approach and an Overview

      • Ranan B. Banerji

      Pages 21-58

   4. GPS and Decision Making: An Overview

      • George W. Ernst

      Pages 59-107

   5. Natural Language Question Answering Systems: 1969

      • Robert F. Simmons

      Pages 108-139

3. Problems in Foundations

   1. Front Matter

      Pages 140-140

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   2. The Role of Weltanschauung in Problem Solving and Inquiry

      • C. West Churchman

      Pages 141-151

   3. Remarks on Mathematics and Computers

      • Hao Wang

      Pages 152-160

   4. Systems Theoretic Approach to Formal Theory of Problem Solving

      • Mihajlo D. Mesarovic

      Pages 161-178

   5. On the Representation of Problems and Goal-Directed Procedures for Computers

      • Saul Amarel

      Pages 179-244

4. Current Research

   1. Front Matter

      Pages 245-245

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   2. Heuristic Search Programs

      • James R. Slagle

      Pages 246-273

   3. Dynamic Programming and Problem-Solving

      • Richard Bellman

      Pages 274-280

   4. Computer Programs can be Proved Correct

      • Ralph L. London

      Pages 281-302

   5. A Computer-Assisted Study of go on M × N Boards

      • Edward Thorp, William E. Walden

      Pages 303-343

   6. Stating Problems as Procedures to a General Problem Solving Program

      • Richard E. Fikes

      Pages 344-361

5. New Applications

   1. Front Matter

      Pages 362-362

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   2. Remarks on the Relationship Between Artificial Intelligence and Cognitive Psychology

      • Allen Newell

      Pages 363-400

   3. A Heuristic Program for Solving a Scientific Inference Problem: Summary of Motivation and Implementation

      • Joshua Lederberg, Georgia L. Sutherland, Bruce G. Buchanan, Edward A. Feigenbaum

      Pages 401-409

Advances in computer technology have pointed out the next important area of computer applications: solution of non-numerical problems. It is hardly necessary to emphasize the importance of these kind of problems. First of all most of the decisions one has to make in real-life situations are non-numerical in the first instance and can be represented as numerical problems only as approximations which are often only partially valid. Second, to use the computer to its full potential it should be employed as a logical machine, capable of deduction, and not just as a numerical calculating machine. Thus the computer would extend man's capability for logical reasoning and not just for his capability to do fast and accurate calculation. It is not a new area; indeed non-numerical problems are central in fields such as artificial intelligence, heuristic programming, pattern recognition, classification and information-processing (and retrival) etc. However, it is fair to assess that progress in the area has not been quite as expected. One of the reasons was a lack of conceptual and theoretical framework in which to investigate different classes of non-numerical problems to improve understanding of various types of problems and methods for their solutions and furthermore to enable the methods which have been proven as effective in one situation to be used in another situation with appropriately similar structure.

• Calculation
• approximation
• mathematics
• problem solving
• theorem

• Systems Research Center, Case Western Reserve University, Cleveland, USA

  R. B. Banerji, M. D. Mesarovic

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