Tuk-tuk: a unified account of similarity judgment and analogical mapping

While similarity and analogy have traditionally been viewed as involving distinct psychological processes, the thesis of this dissertation is that similarity and analogy invoke the same mapping process. This thesis is supported by a growing body of evidence (Markman & Gentner, 1993a, 1993b, 1996; Gentner & Markman, 1997; Goldstone, 1994; Goldstone & Medin, 1994; Larkey & Markman; 2004). The main contribution of this dissertation is a unified account of similarity judgment and analogical mapping. This account is instantiated as Tuk-Tuk, a localist connectionist model of similarity and analogy that determines a mapping between representations via a dynamic process of interactive activation among feature, object, and relation correspondences. Tuk-Tuk differs from extant models of similarity and analogy in its ability to account for both patterns of similarity ratings and benchmark phenomena of analogy. In this dissertation, T'uk-Tuk's performance is tested and contrasted with other models using a broad set of simulations, including simulations of a behavioral study of my own design.

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

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

[3]  M. Gluck.  Stimulus Generalization and Representation in Adaptive Network Models of Category Learning , 1991 .

[4]  D. Gentner,et al.  Introduction : The Place of Analogy in Cognition , 2005 .

[5]  S Imai.  Pattern similarity and cognitive transformations. , 1977, Acta psychologica.

[6]  D. Gentner,et al.  Splitting the Differences: A Structural Alignment View of Similarity , 1993 .

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

[8]  K. Holyoak,et al.  A symbolic-connectionist theory of relational inference and generalization. , 2003, Psychological review.

[9]  I. Biederman.  Human image understanding: Recent research and a theory , 1985, Computer Vision Graphics and Image Processing.

[10]  Marcin Peski.  Categorization , 2006, Encyclopedic Dictionary of Archaeology.

[11]  Patrick Henry Winston,et al.  Learning New Principles from Precedents and Exercises , 1982, Artif. Intell..

[12]  F. Hayes-Roth,et al.  Concept learning and the recognition and classification of exemplars , 1977 .

[13]  Robert M. Nosofsky,et al.  Exemplar-based approach to relating categorization, identification, and recognition , 1992 .

[14]  Dedre Gentner,et al.  Evidence for Relational Selectivity in the Interpretation of Analogy and Metaphor , 1988 .

[15]  C. Krumhansl.  Concerning the Applicability of Geometric Models to Similarity Data : The Interrelationship Between Similarity and Spatial Density , 2005 .

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

[17]  L. R. Novick.  Representational Transfer in Problem Solving , 1990 .

[18]  R. Nosofsky.  Attention, similarity, and the identification-categorization relationship. , 1986, Journal of experimental psychology. General.

[19]  Melanie Mitchell,et al.  Analogy-making as perception - a computer model , 1993, Neural network modeling and connectionism.

[20]  Kenneth D. Forbus,et al.  MAC/FAC: A Model of Similarity-Based Retrieval , 1995, Cogn. Sci..

[21]  Siobhan Chapman.  Logic and Conversation , 2005 .

[22]  A. Tversky.  Features of Similarity , 1977 .

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

[24]  Brian F. Bowdle,et al.  Informativity and Asymmetry in Comparisons , 1997, Cognitive Psychology.

[25]  Dedre Gentner,et al.  Analogy in Scientific Discovery: The Case of Johannes Kepler , 2002 .

[26]  Richard Catrambone,et al.  Is the Self-Concept a Habitual Referent in Judgments of Similarity? , 1996 .

[27]  J. Lackner,et al.  The Psychological Representation of Speech Sounds , 1975, The Quarterly journal of experimental psychology.

[28]  Levi B. Larkey,et al.  Categories among Relations , 2004 .

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

[30]  Paul D. Allopenna,et al.  The locus of knowledge effects in concept learning. , 1994, Journal of experimental psychology. Learning, memory, and cognition.

[31]  Zenon W. Pylyshyn,et al.  Connectionism and cognitive architecture: A critical analysis , 1988, Cognition.

[32]  Arthur B. Markman,et al.  The Fate of Irrelevant Information in Analogical Mapping , 2001 .

[33]  Joshua B. Tenenbaum,et al.  Learning the Structure of Similarity , 1995, NIPS.

[34]  Laura R. Novick,et al.  Component processes in analogical transfer: Mapping, pattern completion, and adaptation. , 1994 .

[35]  B. Indurkhya,et al.  Metaphor and Cognition: An Interactionist Approach , 1993, CL.

[36]  Dedre Gentner,et al.  Systematicity as a Selection Constraint in Analogical Mapping , 1991, Cogn. Sci..

[37]  Richard J. Vondruska,et al.  Salience, similes, and the asymmetry of similarity , 1985 .

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

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

[40]  Allan Collins,et al.  Afterword: comments on parts I, II, and III: a framework for a theory of comparison and mapping , 1989 .

[41]  James L. McClelland,et al.  An interactive activation model of context effects in letter perception: part 1.: an account of basic findings , 1988 .

[42]  Arthur B. Markman,et al.  Similarity is like analogy: Structural alignment in comparison , 1995 .

[43]  E. Rosch,et al.  Family resemblances: Studies in the internal structure of categories , 1975, Cognitive Psychology.

[44]  Douglas J. Gillan,et al.  Reasoning in the Chimpanzee: I. Analogical Reasoning , 1981 .

[45]  Dedre Gentner,et al.  Transfer of training as analogical mapping , 1988, IEEE Trans. Syst. Man Cybern..

[46]  F. Keil.  Concepts, Kinds, and Cognitive Development , 1989 .

[47]  Walter Kintsch,et al.  Toward a model of text comprehension and production. , 1978 .

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

[49]  D. Gentner.  Structure‐Mapping: A Theoretical Framework for Analogy* , 1983 .

[50]  Jeffrey N. Rouder,et al.  A Structural Account of Global and Local Processing , 1999, Cognitive Psychology.

[51]  Janet L. Kolodner,et al.  Case-Based Reasoning , 1988, IJCAI 1989.

[52]  D. Gentner,et al.  Flowing waters or teeming crowds: Mental models of electricity , 1982 .

[53]  W. R. Garner,et al.  Reaction time as a measure of inter- and intraobject visual similarity: Letters of the alphabet , 1979 .

[54]  M. Bassok.  Transfer of domain-specific problem-solving procedures , 1990 .

[55]  G. Lakoff,et al.  Metaphors We Live by , 1981 .

[56]  Robert L. Goldstone,et al.  Relational similarity and the nonindependence of features in similarity judgments , 1991, Cognitive Psychology.

[57]  Barbara A. Spellman,et al.  If Saddam is Hitler then who is George Bush? Analogical mapping between systems of social roles , 1992 .

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

[59]  A. Tversky,et al.  Representations of qualitative and quantitative dimensions. , 1982, Journal of experimental psychology. Human perception and performance.

[60]  D. Medin,et al.  The role of theories in conceptual coherence. , 1985, Psychological review.

[61]  K. Dunbar.  HOW SCIENTISTS REALLY REASON: SCIENTIFIC REASONING IN REAL-WORLD LABORATORIES , 1995 .

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

[63]  Toward an understanding of analogy within a biological symbol system. , 2001 .

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

[65]  Stephen K. Reed,et al.  Pattern recognition and categorization , 1972 .

[66]  Bradley C. Love,et al.  CAB: Connectionist Analogy Builder , 2003, Cogn. Sci..

[67]  Marvin Minsky,et al.  A framework for representing knowledge , 1974 .

[68]  D. Hofstadter.  Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought, Douglas Hofstadter. 1994. Basic Books, New York, NY. 512 pages. ISBN: 0-465-05154-5. $30.00 , 1995 .

[69]  Douglas Hofstadter,et al.  The Copycat Project: An Experiment in Nondeterminism and Creative Analogies , 1984 .

[70]  Robert L. Goldstone,et al.  Comparison and Choice: Relations between Similarity Processes and Decision Processes , 1995 .

[71]  R. Nosofsky.  Stimulus bias, asymmetric similarity, and classification , 1991, Cognitive Psychology.

[72]  Mark T. Keane,et al.  Similarity Processing Depends on the Similarities Present: Effects of Relational Prominence in Similarity and Analogical Processing , 2001 .

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

[74]  Leonard Talmy,et al.  Figure and Ground in Complex Sentences , 1975 .

[75]  Robert L. Goldstone.  Similarity, interactive activation, and mapping , 1994 .

[76]  Douglas L. Medin,et al.  Context theory of classification learning. , 1978 .

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

[78]  John E. Hummel,et al.  Where View-based Theories Break Down: The Role of Structure in Shape Perception and Object Recognition , 2000 .

[79]  D. Gentner,et al.  Structure mapping in the comparison process. , 2000, The American journal of psychology.

[80]  W. Jay Dowling,et al.  Scale structure and similarity of melodies. , 1988 .

[81]  K. Dunbar,et al.  Analogy use in naturalistic settings: The influence of audience, emotion, and goals , 2001, Memory & cognition.

[82]  Patrick Henry Winston,et al.  Learning and reasoning by analogy , 1980, CACM.

[83]  Kurt VanLehn,et al.  Planning Nets: A Representation for Formalizing Analogies and Semantic Models of Procedural Skills. , 1978 .

[84]  U. Hasson,et al.  The importance of being nonalignable: a critical test of the structural alignment theory of similarity. , 2004, Journal of experimental psychology. Learning, memory, and cognition.

[85]  Refractor.  Vision , 2000, The Lancet.

[86]  Robert L. Goldstone,et al.  Similarity Involving Attributes and Relations: Judgments of Similarity and Difference Are Not Inverses , 1990 .

[87]  William M. Bart,et al.  An analysis of generative representation systems , 1980 .

[88]  E. Rosch.  Cognitive reference points , 1975, Cognitive Psychology.

[89]  Tomaso Poggio,et al.  Cooperative computation of stereo disparity , 1988 .

[90]  R. Shepard.  The analysis of proximities: Multidimensional scaling with an unknown distance function. I. , 1962 .

[91]  M. Posner,et al.  On the genesis of abstract ideas. , 1968, Journal of experimental psychology.

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

[93]  D. Gentner,et al.  PSYCHOLOGICAL SCIENCE Research Article THE EFFECTS OF ALIGNABILITY ON MEMORY , 2022 .

[94]  Moshe Burstein,et al.  Concept formatio n by incremental analogica l reasoning and debugging , 1983 .

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

[96]  R. Shepard.  Representation of structure in similarity data: Problems and prospects , 1974 .

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

[98]  R. Shepard,et al.  Toward a universal law of generalization for psychological science. , 1987, Science.

[99]  Kenneth D. Forbus,et al.  Analogy and creativity in the works of Johannes Kepler , 1997 .

[100]  Edward E. Smith,et al.  Category-Based Induction , 1990 .

[101]  G C Gilmore,et al.  Multidimensional letter similarity derived from recognition errors , 1979, Perception & psychophysics.

[102]  D. Gentner,et al.  USE OF STRUCTURE MAPPING THEORY FOR COMPLEX SYSTEMS. , 1986 .

[103]  Arthur B. Markman,et al.  Knowledge Representation , 1998 .

[104]  Yeshayahu Shen,et al.  Symmetric and asymmetric comparisons , 1989 .

[105]  F ATTNEAVE,et al.  Dimensions of similarity. , 1950, The American journal of psychology.

[106]  Kenneth D. Forbus,et al.  Making SME greedy and pragmatic , 2006 .

[107]  E. Holman.  Monotonic models for asymmetric proximities , 1979 .

[108]  Robert L. Goldstone,et al.  Time Course of Comparison , 1994 .

[109]  Roger N. Shepard,et al.  Additive clustering: Representation of similarities as combinations of discrete overlapping properties. , 1979 .

[110]  Richard Gonzalez,et al.  Rating the similarity of simple perceptual stimuli: asymmetries induced by manipulating exposure frequency , 2002, Cognition.

[111]  Eunsook Hong,et al.  Mental Models in Word Problem Solving: An Analysis of Korean Elementary Students. , 1993 .

[112]  Robert L. Goldstone,et al.  Alignment-based nonmonotonicities in similarity. , 1996, Journal of experimental psychology. Learning, memory, and cognition.

[113]  Bipin Indurkhya,et al.  Constrained Semantic Transference: A formal theory of metaphors , 1986, Synthese.

[114]  T. Trabasso,et al.  Causal thinking and the representation of narrative events , 1985 .

[115]  Michael D. Lee,et al.  Combining Dimensions and Features in Similarity-Based Representations , 2002, NIPS.

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

[117]  W. James.  Psychology: Briefer Course , 2020 .

[118]  Kenneth D. Forbus,et al.  A Theory of Rerepresentation in Analogical Matching , 2003 .

[119]  W. S. Merwin,et al.  Selected Translations 1948-1968 , 1970 .

[120]  D. Gentner,et al.  Language and the career of similarity. , 1991 .

[121]  A. Markman,et al.  Structural alignment in similarity and difference judgments , 1996, Psychonomic bulletin & review.

[122]  K. Holyoak,et al.  Social reference points , 1983 .

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

[124]  L. Shastri,et al.  From simple associations to systematic reasoning: A connectionist representation of rules, variables and dynamic bindings using temporal synchrony , 1993, Behavioral and Brain Sciences.

[125]  A. Ortony.  Beyond Literal Similarity , 1979 .

[126]  D. Gentner,et al.  Commonalities and differences in similarity comparisons , 1996, Memory & cognition.

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

[128]  D. Gentner.  Metaphor as Structure Mapping: The Relational Shift. , 1988 .

[129]  A. Tversky,et al.  Similarity, separability, and the triangle inequality. , 1982, Psychological review.

[130]  Douglas L. Hintzman,et al.  "Schema Abstraction" in a Multiple-Trace Memory Model , 1986 .

[131]  G. Marcus.  Rethinking Eliminative Connectionism , 1998, Cognitive Psychology.

[132]  Miriam Bassok,et al.  Adding apples and oranges : Semantic constraints on application of formal rules , 1998 .