A Closer Look at Structural Similarity in Analogical Transfer1

We propose to characterize structural similarity between source and target problems by the type and size of their structural overlap. Size of structural overlap is captured by a measure of graph-distance. We investigated the influence of structural overlap on transfer success in analogical problem solving in two experiments. In both experiments, for a fixed source problem one of five target problems had to be solved. In the first experiment, target problems varied in superficial and structural similarity to the source. In the case of isomorphic source/target relations superficial similarity had no impact on transfer success while for a partial isomorphic target solution success was only high if source and target had identical surface attributes. In the second experiment, surface of source and target were kept identical and different types of structural source/target relations were investigated: For problems with a high structural overlap source inclusive and target exhaustive source/target relations led both to high transfer success. For partial isomorphic problems with a decrease in structural overlap we could show that transfer was successful as long as the common part of source and target was larger than their different parts.

[1]  Allen Newell,et al.  Elements of a theory of human problem solving. , 1958 .

[2]  M. Scheerer,et al.  Problem Solving , 1967, Nature.

[3]  Allen Newell,et al.  Human Problem Solving. , 1973 .

[4]  Stephen K. Reed,et al.  The role of analogy in transfer between similar problem states , 1974 .

[5]  Michael E Atwood,et al.  A process model for water jug problems , 1976, Cognitive Psychology.

[6]  Herbert A Simon,et al.  The understanding process: Problem isomorphs , 1976, Cognitive Psychology.

[7]  K. Holyoak,et al.  Analogical problem solving , 1980, Cognitive Psychology.

[8]  Dedre Gentner,et al.  The Structure of Analogical Models in Science. , 1980 .

[9]  Donald A. Norman,et al.  Analogical Processes in Learning , 1980 .

[10]  K. Holyoak,et al.  Schema induction and analogical transfer , 1983, Cognitive Psychology.

[11]  Dedre Gentner,et al.  Structure-Mapping: A Theoretical Framework for Analogy , 1983, Cogn. Sci..

[12]  P. Pirolli,et al.  The role of learning from examples in the acquisition of recursive programming skills. , 1985 .

[13]  D. Gentner,et al.  Analogical access-a good match is hard to find. 2 , 1986 .

[14]  K. Holyoak,et al.  Surface and structural similarity in analogical transfer , 1987, Memory & cognition.

[15]  L. R. Novick Analogical transfer, problem similarity, and expertise. , 1988, Journal of experimental psychology. Learning, memory, and cognition.

[16]  John R. Anderson,et al.  Use of analogy in a production system architecture , 1989 .

[17]  Brian Falkenhainer,et al.  The Structure-Mapping Engine: Algorithm and Examples , 1989, Artif. Intell..

[18]  B. Ross Distinguishing Types of Superficial Similarities: Different Effects on the Access and Use of Earlier Problems , 1989 .

[19]  Paul Thagard,et al.  Analogical Mapping by Constraint Satisfaction , 1989, Cogn. Sci..

[20]  Stella Vosniadou,et al.  Similarity and analogical reasoning: a synthesis , 1989 .

[21]  Stella Vosniadou,et al.  Similarity and analogical reasoning: Similarity and Analogical Reasoning , 1989 .

[22]  Stephen K. Reed,et al.  Selecting analogous problems: Similarity versus inclusiveness , 1990, Memory & cognition.

[23]  K. Holyoak,et al.  Mathematical problem solving by analogy. , 1991, Journal of experimental psychology. Learning, memory, and cognition.

[24]  Sylvia Weber Russell The Structure-Mapping Engine: Algorithm and Examples (Book) , 1992 .

[25]  Jaime G. Carbonell,et al.  Derivational analogy: a theory of reconstructive problem solving and expertise acquisition , 1993 .

[26]  Kenneth D. Forbus,et al.  The Roles of Similarity in Transfer: Separating Retrievability From Inferential Soundness , 1993, Cognitive Psychology.

[27]  Horst Bunke,et al.  Similarity Measures for Structured Representations , 1993, EWCBR.

[28]  Kurt VanLehn,et al.  Better Learners Use Analogical Problem Solving Sparingly , 1993, ICML.

[29]  L. R. Novick,et al.  Transferring symbolic representations across nonisomorphic problems. , 1994 .

[30]  Mark T. Keane Constraints on Analogical Mapping: A Comparison of Three Models , 1994, Cogn. Sci..

[31]  Douglas R. Hofstadter,et al.  Fluid Concepts and Creative Analogies , 1995 .

[32]  K. Holyoak,et al.  Pragmatics in Analogical Mapping , 1996, Cognitive Psychology.

[33]  Mark T. Keane On Adaptation in Analogy: Tests of Pragmatic Importance and Adaptability in Analogical Problem Solving , 1996 .

[34]  P. Reimann,et al.  Turning examples into cases: Acquiring knowledge structures for analogical problem solving , 1996 .

[35]  B. Ross,et al.  Content Effects in Problem Categorization and Problem Solving , 1996 .

[36]  B. Gholson,et al.  The Sources of Children's Reasoning Errors During Analogical Problem Solving , 1996 .

[37]  Evelyne Clément Knowledge of Domain Effects in Problem Representation: The Case of Tower of Hanoi Isomorphs , 1997 .

[38]  John E. Hummel,et al.  Distributed representations of structure: A theory of analogical access and mapping. , 1997 .

[39]  Fritz Wysotzki,et al.  Induction of Recursive Program Schemes , 1998, ECML.

[40]  Kristina Schädler,et al.  Application of a neural net in classification and knowledge discovery , 1998, ESANN.

[41]  Arthur B. Markman,et al.  Analogy just looks like high level perception: why a domain-general approach to analogical mapping is right , 1998, J. Exp. Theor. Artif. Intell..

[42]  Stephen K. Reed,et al.  Use of examples and procedures in problem solving , 1991 .

[43]  D. Gentner,et al.  The analogical mind : perspectives from cognitive science , 2001 .