Analogy as a means of discovery in problem solving and learning
James Curie Munyer · 1981
It is argued that learning and problem solving are closely related by virtue of their common element of discovery. Analogy is studied as a means of discovery for both these processes. A set of procedures is presented which form a method for reasoning by analogy in which learning follows naturally from problem solving. This is done in the domain of logical deduction although much of the theory is applicable to more general domains. Eight algorithms are presented to implement this method. An analogy matching algorithm constructs partial syntactic matches between predicate calculus formulas. The matches are represented by local maps which are associations between individual symbols, allowing the match to be used as a transformation. The analogical inference rule uses an analogy match in place of unification to directly but inexactly apply a stored derivation to a new problem in order to obtain a plan for its solution. The plan is not in general correct and complete but it can serve to guide a correct derivation and can result in an exponential reduction in search effort by suggesting intermediate steps. Algorithms are presented for handling this inexact deduction while preserving logical validity as an identifiable special case. Logical completeness is also preserved. A plan correction rule is used to suggest corrections based on a near-miss with a valid deduction while attempting to verify a plan. Solutions obtained by analogy are generalized according to the analogy used at each formula. Structural generalizations in the derivations, such as loops, branches, and subroutines, also result from the analogy. Several examples are presented showing how generalized derivations can behave as plans, strategies, heuristics, or tactics in solving further problems. It is believed that a data base of these generalizations accumulated during the process of problem solving will be a practical model for expertise.