Geometric Representations for Minimalist Grammars

  • Authors:

  • Peter Beim Graben;Sabrina Gerth

  • Affiliations:

  • Department of German Language and Linguistics, Bernstein Center for Computational Neuroscience, Humboldt-Universität zu Berlin, Berlin, Germany 10099;Department of Linguistics, University of Potsdam, Potsdam, Germany

  • Venue:
  • Journal of Logic, Language and Information
  • Year:
  • 2012

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Abstract

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.