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Toward a Theory of Problem Solving

  • D. Mandrioli
  • A. Sangiovanni Vincentelli
  • M. Somalvico
Part of the International Centre for Mechanical Sciences book series (CISM, volume 256)

Abstract

The new research activity, which has been developed within the area of artificial intelligence, in general, and within the domain of problem solving, in particular, has awakened the need for a new theoretical effort centered around the notion of problem which more and more appears to be of central importance within computer science.

The studies about the theory of problem solving to which belongs the algebraic approach that we shall present in this paper, are intended to achieve the following main goals:
  • a rather precise understanding of the human behaviour in problem solving;

  • a clear definition of what we mean by an automatic problem solver (APS);

  • a proposal of an internal structure of an automatic problem solver which can perform the three activities of selection, search, and learning;

  • a constructive comparison between the theoretical possibility of an absolutely general automatic problem solver and the practical requirement of a tool useful for the man;

  • the formulation of a theory of problems which can be helpful as a theoretical base in the design of an automatic problem solver.

  • further investigations about the automatic problem solver as a non-deterministic interpreter of an high-level representation language, and as an automatic programmer.

  • naive description of problem solving;

  • algebraic framework for the illustration of the main notions and properties involved both in problem representation and in solution search;

  • extended formalization for the description of a more informed problem representation;

  • automatic evaluation and use of heuristic information for improving the efficiency of the solution search;

  • generalization and development of a learning ability during the problem-solving activity.

More precisely, the purpose of this paper is to present the results which have been obtained, within the Milan Polytechnic Artificial Intelligence Project (MP-AI Project), by the authors in developing such a theory of problem solving, in the last two years.

The notions, which will be presented, can be briefly sketched as follows:
  • naive description of problem solving;

  • algebraic framework for the illustration of the main notions and properties involved both in problem representation and in solution search;

  • extended formalization for the description of a more informed problem representation;

  • automatic evaluation and use of heuristic information for improving the efficiency of the solution search;

  • generalization and development of a learning ability during the problem-solving activity.

The presented results provide more understanding of some focal points on which a theory of problem solving can be founded.

Such a theory will constitute a formal basis for the design of automatic problem solvers, intended as the interpreters of the representation languages in which the represented problems have been communicated to the computer.

Keywords

Goal Node Problem Solver Heuristic Function Solution Sequence Semantic Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1976

Authors and Affiliations

  • D. Mandrioli
    • 1
  • A. Sangiovanni Vincentelli
    • 1
  • M. Somalvico
    • 1
  1. 1.Milan Polytechnic Artificial Intelligence ProjectMP-AI ProjectMilanItaly

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