Integrating analogical mapping and general problem solving: the path-mapping theory

This article describes the path-mapping theory of how humans integrate analogical mapping and general problem solving. The theory posits that humans represent analogs with declarative roles, map analogs by lower-level retrieval of analogous role paths, and coordinate mappings with higher-level organizational knowledge. Implemented in the ACT-R cognitive architecture, the path-mapping theory allows models of analogical mapping behavior to incorporate and interface with other problem-solving knowledge. Path-mapping models thus can include task-specific skills such as encoding analogs and generating responses, and can make behavioral predictions at the level of real-world metrics such as latency or correctness. We show that the path-mapping theory can successfully account for the major phenomena addressed by previous theories of analogy. We also demonstrate a path-mapping model that can account for subjectsÕ incremental eye-movement and typing behavior in a story-mapping task. We discuss extensions and implications of this work to other areas of analogy and problem-solving research. Salvucci & Anderson, Integrating Mapping and Problem Solving 3

[1]  K. Rayner.  Eye Movements and Cognitive Processes in Reading, Visual Search, and Scene Perception , 1995 .

[2]  D. Gentner,et al.  Structure mapping in analogy and similarity. , 1997 .

[3]  K. Holyoak,et al.  Mental Leaps: Analogy in Creative Thought , 1994 .

[4]  Mark T. Keane,et al.  The Incremental Analogy Machine: A Computational Model of Analogy , 1988, EWSL.

[5]  Dedre Gentner,et al.  Mechanisms of Analogical Learning. , 1987 .

[6]  T. Salthouse.  Perceptual, cognitive, and motoric aspects of transcription typing. , 1986, Psychological bulletin.

[7]  M A Just,et al.  From the SelectedWorks of Marcel Adam Just 1990 What one intelligence test measures : A theoretical account of the processing in the Raven Progressive Matrices Test , 2016 .

[8]  Kenneth D. Forbus,et al.  Incremental Structure-Mapping , 2019, Proceedings of the Sixteenth Annual Conference of the Cognitive Science Society.

[9]  Giyoo Hatano,et al.  Young Children's Spontaneous Personification as Analogy. , 1987 .

[10]  C. Lebiere,et al.  Models of Working Memory: Modeling Working Memory in a Unified Architecture: An ACT-R Perspective , 1999 .

[11]  Richard Reviewer-Granger.  Unified Theories of Cognition , 1991, Journal of Cognitive Neuroscience.

[12]  G. Halford.  Analogical Reasoning and Conceptual Complexity in Cognitive Development , 1992 .

[13]  D. Gentner,et al.  PSYCHOLOGICAL SCIENCE Research Article STRUCTURAL ALIGNMENT IN COMPARISON: No Difference Without Similarity , 2022 .

[14]  B. Ross.  This is like that: The use of earlier problems and the separation of similarity effects. , 1987 .

[15]  Arthur B. Markman,et al.  Constraints on Analogical Inference , 1997, Cogn. Sci..

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

[17]  Dedre Gentner,et al.  ANALOGICAL REMINDING: A GOOD MATCH IS HARD TO FIND. , 1985 .

[18]  C. Lebiere,et al.  An integrated theory of list memory. , 1998 .

[19]  M. Burstein.  Combining Analogies in Mental Models , 1988 .

[20]  R. Catrambone.  Improving examples to improve transfer to novel problems , 1994, Memory & cognition.

[21]  John H. Holland,et al.  Induction: Processes of Inference, Learning, and Discovery , 1987, IEEE Expert.

[22]  P. Langley,et al.  Production system models of learning and development , 1987 .

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

[24]  J. Grudin.  Processes in Verbal Analogy Solution. , 1980 .

[25]  G. McConkie,et al.  Integrating information across eye movements , 1980, Cognitive Psychology.

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

[27]  D E Kieras,et al.  A computational theory of executive cognitive processes and multiple-task performance: Part 1. Basic mechanisms. , 1997, Psychological review.

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

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

[30]  Lieven Verschaffel,et al.  Influence of the semantic structure of word problems on second graders' eye movements , 1990 .

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

[32]  M. Just,et al.  From the SelectedWorks of Marcel Adam Just 1992 A capacity theory of comprehension : Individual differences in working memory , 2017 .

[33]  Michael Matessa,et al.  A Production System Theory of Serial Memory , 1997 .

[34]  B. Kokinov.  Analogy is like Cognition: Dynamic, Emergent, and Context-Sensitive , 1999 .

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

[36]  A. Miyake,et al.  Models of Working Memory: Mechanisms of Active Maintenance and Executive Control , 1999 .

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

[38]  Kurt VanLehn,et al.  Analogy Events: How Examples are Used During Problem Solving , 1998, Cogn. Sci..

[39]  Brian Falkenhainer,et al.  The Structure-Mapping Engine * , 2003 .

[40]  Mark T. Keane,et al.  Simulating analogical mapping difficulties in recursion problems , 1989 .

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

[42]  D. Gentner,et al.  Advances in Analogy Research: Integration of Theory and Data from the Cognitive, Computational, and Neural Sciences , 1997, Cognitive Psychology.

[43]  B. Ross,et al.  Generalizing from the use of earlier examples in problem solving , 1990 .

[44]  C. Lebiere,et al.  The Atomic Components of Thought , 1998 .

[45]  M. Just,et al.  Eye fixations and cognitive processes , 1976, Cognitive Psychology.

[46]  Mark T. Keane.  What makes an analogy difficult? The effects of order and causal structure on analogical mapping. , 1997, Journal of experimental psychology. Learning, memory, and cognition.

[47]  Tony Veale,et al.  The Competence of Sub-Optimal Theories of STructure Mapping on Hard Analogies , 1997, IJCAI.

[48]  John R. Anderson,et al.  Tracing Eye Movement Protocols with Cognitive Process Models , 1998 .

[49]  D. Gentner,et al.  Structural Alignment during Similarity Comparisons , 1993, Cognitive Psychology.

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

[51]  G. Miller,et al.  Cognitive science. , 1981, Science.

[52]  D. Gentner,et al.  Similarity and the development of rules , 1998, Cognition.

[53]  Dedre Gentner,et al.  Systematicity and Surface Similarity in the Development of Analogy , 1986, Cogn. Sci..

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

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