Solving geometric analogy problems through two-stage analogical mapping

Andrew Lovett*, Emmett Tomai, Kenneth D Forbus, Jeffrey Usher

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

Abstract

Evans' 1968 ANALOGY system was the first computer model of analogy. This paper demonstrates that the structure mapping model of analogy, when combined with high-level visual processing and qualitative representations, can solve the same kinds of geometric analogy problems as were solved by ANALOGY. Importantly, the bulk of the computations are not particular to the model of this task but are general purpose: We use our existing sketch understanding system, CogSketch, to compute visual structure that is used by our existing analogical matcher, Structure Mapping Engine (SME). We show how SME can be used to facilitate high-level visual matching, proposing a role for structural alignment in mental rotation. We show how second-order analogies over differences computed via analogies between pictures provide a more elegant model of the geometric analogy task. We compare our model against human data on a set of problems, showing that the model aligns well with both the answers chosen by people and the reaction times required to choose the answers.

Original languageEnglish (US)
Pages (from-to)1192-1231
Number of pages40
JournalCognitive Science
Volume33
Issue number7
DOIs
StatePublished - Sep 1 2009

Keywords

  • Analogy
  • Geometric analogy
  • Symbolic computational modeling

ASJC Scopus subject areas

  • Experimental and Cognitive Psychology
  • Cognitive Neuroscience
  • Artificial Intelligence

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