Cross-Situational Learning: A Mathematical Approach

  • Kenny Smith
  • Andrew D. M. Smith
  • Richard A. Blythe
  • Paul Vogt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4211)


We present a mathematical model of cross-situational learning, in which we quantify the learnability of words and vocabularies. We find that high levels of uncertainty are not an impediment to learning single words or whole vocabulary systems, as long as the level of uncertainty is somewhat lower than the total number of meanings in the system. We further note that even large vocabularies are learnable through cross-situational learning.


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  1. 1.
    Hockett, C.F.: The origin of speech. Scientific American 203, 88–96 (1960)CrossRefGoogle Scholar
  2. 2.
    Carey, S., Bartlett, E.: Acquiring a single new word. Papers and Reports on Child Language Development 15, 17–29 (1978)Google Scholar
  3. 3.
    Quine, W.v.O.: Word and Object. MIT Press, Cambridge (1960)zbMATHGoogle Scholar
  4. 4.
    Bloom, P.: How Children Learn the Meanings of Words. MIT Press, Cambridge (2000)Google Scholar
  5. 5.
    Hall, D.G., Waxman, S.R. (eds.): Weaving a Lexicon. MIT Press, Cambridge (2004)Google Scholar
  6. 6.
    Tomasello, M.: The cultural origins of human cognition. Harvard University Press, Harvard (1999)Google Scholar
  7. 7.
    Tomasello, M.: Constructing a language: a usage-based theory of language acquisition. Harvard University Press, Harvard (2003)Google Scholar
  8. 8.
    Macnamara, J.: Names for things: a study of human learning. MIT Press, Cambridge (1982)Google Scholar
  9. 9.
    Landau, B., Smith, L.B., Jones, S.S.: The importance of shape in early lexical learning. Cognitive Development 3, 299–321 (1988)CrossRefGoogle Scholar
  10. 10.
    Markman, E.M.: Categorization and naming in children: problems of induction. In: Learning, Development and Conceptual Change. MIT Press, Cambridge (1989)Google Scholar
  11. 11.
    Clark, E.V.: The lexicon in acquisition. In: Cambridge Studies in Linguistics. Cambridge University Press, Cambridge (1993)Google Scholar
  12. 12.
    Akhtar, N., Montague, L.: Early lexical acquisition: the role of cross-situational learning. First Language, 347–358 (1999)Google Scholar
  13. 13.
    Klibanoff, R.S., Waxman, S.R.: Basic level object categories support the acquisition of novel adjectives: evidence from pre-school aged children. Child Development 71(3), 649–659 (2000)CrossRefGoogle Scholar
  14. 14.
    Houston-Price, C., Plunkett, K., Harris, P.: ‘Word-Learning Wizardry’ at 1;6. Journal of Child Language 32(1), 175–189 (2005)CrossRefGoogle Scholar
  15. 15.
    Smith, A.D.M.: Establishing communication systems without explicit meaning transmission. In: Kelemen, J., Sosík, P. (eds.) Advances in Artificial Life, pp. 381–390. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  16. 16.
    Vogt, P., Coumans, H.: Investigating social interaction strategies for bootstrapping lexicon development. Journal of Artificial Societies and Social Simulation 6(1) (2003),
  17. 17.
    Siskind, J.M.: A computational study of cross-situational techniques for learning word-to-meaning mappings. Cognition 61, 39–91 (1996)CrossRefGoogle Scholar
  18. 18.
    Smith, A.D.M.: Intelligent meaning creation in a clumpy world helps communication. Artificial Life 9(2), 175–190 (2003)CrossRefGoogle Scholar
  19. 19.
    Zipf, G.K.: The Psycho-Biology of Language. Routledge, London (1936)Google Scholar
  20. 20.
    Wilf, H.S.: Generatingfunctionology. Academic Press, London (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kenny Smith
    • 1
  • Andrew D. M. Smith
    • 1
  • Richard A. Blythe
    • 2
  • Paul Vogt
    • 1
    • 3
  1. 1.Language Evolution and Computation Research UnitUniversity of Edinburgh 
  2. 2.School of PhysicsUniversity of Edinburgh 
  3. 3.ILK/Language and Information ScienceTilburg UniversityThe Netherlands

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