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Article published In: The Mental Lexicon
Vol. 13:2 (2018) ► pp.230–268

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Methodological and analytic considerations

Inflectional morphology with linear mappings

 | University of Tübingen
 | University of Tübingen
 | University of Cambridge
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Available under the Creative Commons Attribution (CC BY) 4.0 license.

For any use beyond this license, please contact the publisher at rights@benjamins.nl.

Published online: 10 January 2019
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https://doi.org/10.1075/ml.18010.baa
Abstract
This methodological study provides a step-by-step introduction to a computational implementation of word and paradigm morphology using linear mappings between vector spaces for form and meaning. Taking as starting point the linear regression model, the main concepts underlying linear mappings are introduced and illustrated with R code. It is then shown how vector spaces can be set up for Latin verb conjugations, using 672 inflected variants of two verbs each from the four main conjugation classes. It turns out that mappings from form to meaning (comprehension), and from meaning to form (production) can be carried out loss-free. This study concludes with a demonstration that when the graph of triphones, the units that underlie the form space, is mapped onto a 2-dimensional space with a self-organising algorithm from physics (graphopt), morphological functions show topological clustering, even though morphemic units do not play any role whatsoever in the model. It follows, first, that evidence for morphemes emerging from experimental studies using, for instance, fMRI, to localize morphemes in the brain, does not guarantee the existence of morphemes in the brain, and second, that potential topological organization of morphological form in the cortex may depend to a high degree on the morphological system of a language.
Article outline
  • 1.Introduction
  • 2.Latin conjugations
  • 3.Introduction to the mathematics of linear mappings
  • 4.Matrices for form and meaning in Latin
  • 5.Mappings between form and meaning
    • 5.1Comprehension: From form to meaning
    • 5.2Production: from meaning to form
  • 6.A novel perspective on traditional evidence for morphemes
  • 7.Concluding remarks
  • References
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