Geometric Representations for Minimalist Grammars

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.

• Publication year

  2011

• Venue

  Journal of Logic, Language and Information

• Publication date

  2011-01-26

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1007/s10849-012-9164-2arXiv 1101.5076
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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